Dissertations / Theses: 'Differential inclusions'

1

Bian, Wenming. "Operator inclusions and operator-differential inclusions." Thesis, University of Glasgow, 1998. http://theses.gla.ac.uk/2029/.

Full text

Abstract:

In Chapter 2, we first introduce a generalized inverse differentiability for set-valued mappings and consider some of its properties. Then, we use this differentiability, Ekeland's Variational Principle and some fixed point theorems to consider constrained implicit function and open mapping theorems and surjectivity problems of set-valued mappings. The mapping considered is of the form F(x, u) + G (x, u). The inverse derivative condition is only imposed on the mapping x F(x, u), and the mapping x G(x, u) is supposed to be Lipschitz. The constraint made to the variable x is a closed convex cone if x F(x, u) is only a closed mapping, and in case x F(x, u) is also Lipschitz, the constraint needs only to be a closed subset. We obtain some constrained implicit function theorems and open mapping theorems. Pseudo-Lipschitz property and surjectivity of the implicit functions are also obtained. As applications of the obtained results, we also consider both local constrained controllability of nonlinear systems and constrained global controllability of semilinear systems. The constraint made to the control is a time-dependent closed convex cone with possibly empty interior. Our results show that the controllability will be realized if some suitable associated linear systems are constrained controllable. In Chapter 3, without defining topological degree for set-valued mappings of monotone type, we consider the solvability of the operator inclusion y0 N1(x) + N2 (x) on bounded subsets in Banach spaces with N1 a demicontinuous set-valued mapping which is either of class (S+) or pseudo-monotone or quasi-monotone, and N2 is a set-valued quasi-monotone mapping. Conclusions similar to the invariance under admissible homotopy of topological degree are obtained. Some concrete existence results and applications to some boundary value problems, integral inclusions and controllability of a nonlinear system are also given. In Chapter 4, we will suppose u A (t,u) is a set-valued pseudo-monotone mapping and consider the evolution inclusions x' (t) + A(t,x((t)) f (t) a.e. and (d)/(dt) (Bx(t)) + A (t,x((t)) f(t) a.e. in an evolution triple (V,H,V*), as well as perturbation problems of those two inclusions.

APA, Harvard, Vancouver, ISO, and other styles

2

Chen, Xiaoli. "Stochastic differential inclusions." Thesis, University of Edinburgh, 2006. http://hdl.handle.net/1842/13367.

Full text

Abstract:

Stochastic differential inclusions (SDIs) on Rd have been investigated in this thesis, dx(t) Î a(t, x(t))dt + (t, x (t)d where a is a maximal monotone mapping, b is a Lipschitz continuous function, and w is a Wiener process. The principal aim of this work is to present some new results on solvability and approximations of SDIs. Two methods are adapted to obtain our results: the method of minimization and the method of implicit approximation. We interpret the method of monotonicity as a method of constructing minimizers to certain convex functions. Under the monotonicity condition and the usual linear growth condition, the solutions are characterized as the minimizers of convex functionals, and are constructed via implicit approximations. Implicit numerical scheme is given and the result on the rate of convergence is also presented. The ideas of our work are inspired by N.V. Krylov, where stochastic differential equations (SDEs0 in Rd are solved by minimizing convex functions via Euler approximations. Furthermore, since the linear growth condition is too strong, an approach is proposed for truncating maximal monotone functions to get bounded maximal monotone functions. It is a technical challenge in this thesis. Thus the existence of solutions to SDIs is proved under essentially weaker growth condition than the linear growth. For a special case of SDEs, a few of recent results from [5] are generalized. Some existing results of the convergence by implicit numerical schemes are proved under the locally Lipschitz condition. We will show that under certain weaker conditions, if the drift coefficient satisfies one-sided Lipschitz and the diffusion coefficient is Lipschitz continuous, implicit approximations applied to SDEs, converge almost surely to the solution of SDEs. The rate of convergence we get is ¼.

APA, Harvard, Vancouver, ISO, and other styles

3

Bauwe, Anne, and Wilfried Grecksch. "Finite dimensional stochastic differential inclusions." Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800515.

Full text

Abstract:

This paper offers an existence result for finite dimensional stochastic differential inclusions with maximal monotone drift and diffusion terms. Kravets studied only set-valued drifts in [5], whereas Motyl [4] additionally observed set-valued diffusions in an infinite dimensional context. In the proof we make use of the Yosida approximation of maximal monotone operators to achieve stochastic differential equations which are solvable by a theorem of Krylov and Rozovskij [7]. The selection property is verified with certain properties of the considered set-valued maps. Concerning Lipschitz continuous set-valued diffusion terms, uniqueness holds. At last two examples for application are given.

APA, Harvard, Vancouver, ISO, and other styles

4

Palladino, Michele. "Optimal control of differential inclusions." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/25271.

Full text

Abstract:

The thesis concerns some recent advances on necessary conditions for optimal control problems, paying particular attention to the case in which the velocity constraint is expressed in terms of a multifunction. In the first part of the thesis we have explored the link which arises between relaxation and first order necessary conditions. Relaxation is a widely used regularization procedure in optimal control, involving the replacement of velocity sets by their convex hulls, to ensure the existence of a minimizer. It turns out that some pathological situations arise in which the costs of relaxed and original problems do not coincide (infimum gap conditions). In this case, we cannot obtain approximate solution of the optimal control problem of interest. In particular, we show how necessary conditions expressed in terms of Fully Convexified Hamiltonian Inclusion are a↵ected by the presence of an infimum gap. Applications of these results are showed also in the case in which the velocity constraint is expressed in terms of controlled di↵erential equations. In the second part of the thesis we study the regularity of the Hamiltonian along the optimal trajectory for problems with state constraint. Two applications of these properties are demonstrated. One is to derive improved conditions which guarantee the nondegeneracy of necessary conditions of optimality, in the form of a Hamiltonian inclusion. The other application is to derive new, less restrictive, conditions under which minimizers in the calculus of variations have bounded slope.

APA, Harvard, Vancouver, ISO, and other styles

5

Palombaro, Mariapia. "Solenoidal differential inclusions and H-measures." Doctoral thesis, La Sapienza, 2004. http://hdl.handle.net/11573/917107.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Hosseini, Ali Abadi M. "The Tau method in the solution of differential inclusions and nonlinear partial differential equations." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47111.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Russell, Brandon C. "HOMOGENIZATION IN PERFORATED DOMAINS AND WITH SOFT INCLUSIONS." UKnowledge, 2018. https://uknowledge.uky.edu/math_etds/55.

Full text

Abstract:

In this dissertation, we first provide a short introduction to qualitative homogenization of elliptic equations and systems. We collect relevant and known results regarding elliptic equations and systems with rapidly oscillating, periodic coefficients, which is the classical setting in homogenization of elliptic equations and systems. We extend several classical results to the so called case of perforated domains and consider materials reinforced with soft inclusions. We establish quantitative H1-convergence rates in both settings, and as a result deduce large-scale Lipschitz estimates and Liouville-type estimates for solutions to elliptic systems with rapidly oscillating periodic bounded and measurable coefficients. Finally, we connect these large-scale estimates with local regulartity results at the microscopic-level to achieve interior Lipschitz regularity at every scale.

APA, Harvard, Vancouver, ISO, and other styles

8

Gyrya, Vitaliy T. "Variational problems on domains with inclusions homogenization through [gamma]-convergence /." Akron, OH : University of Akron, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=akron1121462160.

Full text

Abstract:

Thesis (M.S.)--University of Akron, Dept. of Mathematics, 2005. "August, 2005." Title from electronic thesis title page (viewed 11/28/2005) Advisor, Dmitry Golovaty; Faculty Readers, Eric Wright, Curtis B. Clemons; Associate Department Chair, Timothy S. Norfolk; Dean of the College, Charles B. Monroe; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.

APA, Harvard, Vancouver, ISO, and other styles

9

Nguyen, Bao. "Contribution to nonsmooth lyapunov stability of differential inclusions with maximal monotone operators." Tesis, Universidad de Chile, 2017. http://repositorio.uchile.cl/handle/2250/149077.

Full text

Abstract:

Doctor en Ciencias de la Ingeniería, Mención Modelación Matemática en cotutela con la Universidad de Limoges In this PhD thesis, we make some contributions to nonsmooth Lyapunov stability of first-order differential inclusions with maximal monotone operators, in the setting of infinite-dimensional Hilbert spaces. We provide primal and dual explicit characterizations for parameterized weak and strong Lyapunov pairs of lower semicontinuous extended-real-valued functions, referred to as $a-$Lyapunov pairs, associated to differential inclusions with right-hand-sides governed by Lipschitz or Cusco perturbations $F$ of maximal monotone operators $A$, ẋ(t) ∈ F (x(t)) − A(x(t)), t ≥ 0, x(0) ∈ dom A. Equivalently, we study the weak and strong invariance of sets with respect to such differential inclusions. As in the classical Lyapunov approach to the stability of differential equations, the presented results make use of only the data of the differential system; that is, the operator $A$ and the multifunction $F$, and so no need to know about the solutions, nor the semi-groups generated by the monotone operators. Because our Lyapunov pairs and invariant sets candidates are just lower semicontinuous and closed, respectively, we make use of nonsmooth analysis to provide first-order-like criteria using general subdifferentials and normal cones. We provide similar analysis to non-convex differential inclusions governed by proximal normal cones to prox-regular sets. Our analysis above allowed to prove that such apparently more general systems can be easily coined into our convex setting. We also use our results to study the geometry of maximal monotone operators, and specifically, the characterization of the boundary of the values of such operators by means only of the values at nearby points, which are distinct of the reference point. This result has its application in the stability of semi-infinite programming problems. We also use our results on Lyapunov pairs and invariant sets to provide a systematic study of Luenberger-like observers design for differential inclusions with normal cones to prox-regular sets. The thesis is organized as follows: In chapter 1, we explain the main objectives of the thesis, the methodology that we follow, and we give a preview of the main results. We also make in this chapter a general overview of Lyapunov's theory, and present the main previous achievements on the subject. In Chapter 2, we present the main tools and preliminary results that we need in our analysis. In Chapter 3, we give the desired characterizations of Lyapunov pairs and invariant sets for differential inclusions with Lipschitz perturbations of maximal monotone operators, while in Chapter 4, we investigate differential inclusions with Lipschitz perturbations of proximal normal cones. This chapter includes the application to Luenberger-like observers design. In Chapter 5, we study differential inclusions with Lipschitz Cusco perturbations of maximal monotone operators. In Chapter 6, we give a result on the geometry of maximal monotone operators, and describe the boundary of their values. Finally, we give in Chapter 7 a resume of the results we obtained. En esta tesis doctoral se realiza una contribución a la estabilidad de Lyapunov no suave de inclusiones diferenciales de primer orden con operadores maximales monótonos, en el con- texto de espacios de Hilbert de dimensión infinita. Se entregan caracterizaciones primales y duales explícitas para los pares de Lyapunov parametrizados débiles y fuertes de funciones inferiormente semicontinuas con valores extendedidos, referidas como pares a-Lyapunov, aso- ciados a inclusiones diferenciales con un lado derecho gobernado por perturbaciones F de tipo Lipschitz o Cusco de operadores maximales monótonos A, ẋ(t) ∈ F (x(t)) − A(x(t)), t ≥ 0, x(0) ∈ dom A. De manera equivalente, se estudian la invarianza débil y fuerte de conjuntos con respecto a tales inclusiones diferenciales. Tal como en el enfoque clásico de Lyapunov para estudiar la la estabilidad de ecuaciones diferenciales, los resultados presentados usan solamente la información del sistema; es decir, el operador A y la multiaplicación F , y, por lo tanto, no es necesario conocer las soluciones ni el semigrupo generado por el operador monótono. Dado que los pares de Lyapunov y conjuntos invariantes considerados aquí son, respectivamente, inferiormente semicontinuos y cerrados, se utiliza el análisis no-suave para proveer criterios de primer order utilizando subdiferenciales y conos lo suficientemente generales. Se realiza un análisis similar al caso de las inclusiones diferenciales no convexas gobernadas por conos normales proximales a conjuntos prox-regulares. Nuestro análisis permite demostrar que tales sistemas, aparentemente más generales, pueden ser fácilmente acuñados en nuestro con- texto. Además, nuestros resultados son utilizados para estudiar la geometría de operadores maximales monótonos, y específicamente, la caracterización de la frontera de los valores de tales operadores mediante sólo los puntos cercanos, diferentes del punto de referencia. Este resultado tiene aplicaciones en la estabilidad de problemas de programación semi-infinita. Además, nuestros resultados se utilizan en los pares de Lyapunov de conjuntos invariantes para realizar un estudio sistemático del diseño de observadores de tipo Luenberger para in- clusiones diferenciales con conos normales a conjuntos prox-regulares. La tesis está organizada de la siguiente manera: en el Capítulo 1, se explican los principales objetivos de la tesis, la metodología seguida, y se entrega una vista previa de los principales resultados. Además, en este capítulo, se da una visión general de la teoría de Lyapunov, y se presentan los resultados previos en el tema. En el Capítulo 2, se presentan las principales herramientas y los resultados preliminares necesarios en nuestro análisis. En el Capítulo 3, se entregan las caracterizaciones deseadas de los pares de Lyapunov y conjuntos invariantes para inclusiones diferenciales con perturbaciones Lipschitz de operadores maximales monótonos, mientras que en el Capítulo 4, se investigan las inclusiones diferenciales con perturbaciones Lipschitz de conos normales proximales. Este capítulo incluye una aplicación al disenño de observadores de tipo Luenberger. En el Capítulo 5, se estudian inclusiones diferenciales con perturbaciones Lipschitz Cusco de operadores maximales monótonos. En el Capítulo 6, se entrega un resultado sobre la geometría de los operadores maximales monótonos, y se describe la frontera de sus valores. Finalmente, en el Capítulo 7 se da un resumen de los resultados obtenidos.

APA, Harvard, Vancouver, ISO, and other styles

10

Trostorff, Sascha. "Well-posedness and causality for a class of evolutionary inclusions." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-78325.

Full text

Abstract:

We study a class of differential inclusions involving maximal monotone relations, which cover a huge class of problems in mathematical physics. For this purpose we introduce the time derivative as a continuously invertible operator in a suitable Hilbert space. It turns out that this realization is a strictly monotone operator and thus, the question on existence and uniqueness can be answered by well-known results in the theory of maximal monotone relations. Furthermore, we show that the resulting solution operator is Lipschitz-continuous and causal, which is a natural property of evolutionary processes. Finally, the results are applied to a system of partial differential equations and inclusions, which describes the diffusion of a compressible fluid through a saturated, porous, plastically deforming media, where certain hysteresis phenomena are modeled by maximal montone relations.

APA, Harvard, Vancouver, ISO, and other styles

11

Brault, Antoine. "Flots rugueux et inclusions différentielles perturbées." Thesis, Toulouse 3, 2018. http://www.theses.fr/2018TOU30160/document.

Full text

Abstract:

Cette thèse est composée de trois chapitres indépendants ayant pour thématique commune la théorie des trajectoires rugueuses. Introduite en 1998 par Terry Lyons, cette approche trajectorielle des équations différentielles stochastiques (EDS) permet l'étude d'EDS dirigées par des processus n'ayant pas la propriété de semi-martingale nécessaire à l'application du cadre de l'intégration d'Itô. C'est par exemple le cas du mouvement brownien fractionnaire pour un indice de Hurst différent d'un demi. Le premier chapitre porte sur les liens entre la théorie des trajectoires rugueuses et celle des structures de régularité qui a été récemment introduite par Martin Hairer pour résoudre une large classe d'équations aux dérivées partielles stochastiques. Nous exposons, avec les outils de cette nouvelle théorie, la définition de l'intégrale rugueuse et de la signature d'une trajectoire irrégulière, ce qui nous mène à la résolution d'équations différentielles rugueuses (EDR). Dans le second chapitre, nous nous intéressons à la construction de flots d'EDR à partir de leurs approximations en temps petit, appelées presque flots. Nous montrons que sous des conditions faibles de régularité du presque flot, bien que l'unicité des solutions de l'EDR associée ne soit plus assurée, il est possible de sélectionner un flot mesurable. Notre cadre général unifie les précédentes approches par flot dues à I. Bailleul, A. M. Davie, P. Friz et N. Victoir. Le dernier chapitre s'attache à l'étude d'une inclusion différentielle perturbée par une trajectoire rugueuse, c'est-à-dire d'une EDR dont la dérive est une fonction multivaluée. Nous démontrons, sans hypothèse de convexité et avec différentes conditions de régularité sur la dérive, l'existence de solution This thesis consists of three independent chapters in the theme of rough path theory. Introduced in 1998 by Terry Lyons, this pathwise approach to stochastic differential equations (SDE) allows one to study SDE driven by processes that do not have the semi-martingale property which is required to apply the framework of the Itô integral. This is for example the case of the fractional Brownian motion for a Hurst index different from one-half. The first chapter deals with the links between rough path and regularity structure theories. The latter was recently introduced by Martin Hairer to solve a large class of stochastic partial differential equations. With the tools of this new theory, we show how to build the rough integral and the signature of an irregular path, which leads to solve a rough differential equation (RDE). In the second chapter, we focus on building RDE flows from their approximations at small scale, called almost flows. We show that under weak conditions on regularity of almost flows, although the uniqueness of the associated RDE solutions does not hold, we are able to select a measurable flow. Our general framework unifies the previous approaches by flow due to I. Bailleul, A. M. Davie, P. Friz and N. Victoir. In the last chapter, we study of a differential inclusion perturbed by a rough path, i.e. a RDE whose drift is a multivalued function. We prove, without convexity hypothesis and several conditions on the regularity of the drift, the existence of a solution

APA, Harvard, Vancouver, ISO, and other styles

12

Harju, Johansson Janne. "A structure utilizing inexact primal-dual interior-point method for analysis of linear differential inclusions /." Licentiate thesis, Linköping : Department of Electrical Engineering, Linköping University, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11791.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Harker, Shaun Russell. "Classical mechanics with dissipative constraints." Thesis, Montana State University, 2009. http://etd.lib.montana.edu/etd/2009/harker/HarkerS0809.pdf.

Full text

Abstract:

The aim of this thesis is to consider the mathematical treatment of mechanical systems in the presence of constraints which are energetically dissipative. Constraints may be energetically dissipative due to impacts and friction. In the frictionless setting, we generalize Hamilton's principle of stationary action, central to the Lagrangian formulation of classical mechanics, to reflect optimality conditions in constrained spaces. We show that this generalization leads to the standard measure-theoretic equations for shocks in the presence of unilateral constraints. Previously, these equations were simply postulated; we derive them from a fundamental variational principle. We also present results in the frictional setting. We survey the extensive literature on the subject, which focusses on existence results and numerical schemes known as time- stepping algorithms. We consider a novel model of friction (which is more dissipative than standard Coulomb friction) for which we can give better well-posedness results than what is currently available for the Coulomb theory. To this end, we study multi-valued maps, differential inclusions, and optimization theory. We construct a differential inclusion we call the feedback problem, for which the multi-valued map is the solution set of a convex program. We give existence and uniqueness results regarding this feedback problem. We cast the persistent contact evolution problem of our novel model of friction into the form of a feedback problem to derive an existence result.

APA, Harvard, Vancouver, ISO, and other styles

14

Noel, Jimmy. "Inclusions différentielles d'évolution associées à des ensembles sous-lisses." Thesis, Montpellier 2, 2013. http://www.theses.fr/2013MON20010/document.

Full text

Abstract:

Cette thèse est consacrée à l'étude d'existence de solutions pour certains problèmes d'évolution. Il s'agit de processus de rafle perturbés associés d'une part à des ensembles prox-réguliers et d'autre part à des ensembles sous-lisses. Les ensembles sont supposés évoluer de façon lipschitzienne ou absolument continue This dissertation is devoted to the study of the existence of solutions for some evolution problems. The study is concerned with perturbed sweeping processes associated on the one hand with prox-regular sets and the other hand with subsmooth sets. It is assumed that the sets move either in a Lipschitz way or in an absolutely continuous way

APA, Harvard, Vancouver, ISO, and other styles

15

Bernuau, Emmanuel. "Robustesse et stabilité des systèmes non-linéaires : un point de vue basé sur l’homogénéité." Thesis, Ecole centrale de Lille, 2013. http://www.theses.fr/2013ECLI0015/document.

Full text

Abstract:

L'objet de ce travail est l’étude des propriétés de stabilité et de robustesse des systèmes non-linéaires via des méthodes basées sur l'homogénéité. Dans un premier temps, nous rappelons le contexte usuel des systèmes homogènes ainsi que leurs caractéristiques principales. La suite du travail porte sur l'extension de l'homogénéisation des systèmes non-linéaires, déjà proposée dans le cadre de l'homogénéité à poids, au cadre plus général de l'homogénéité géométrique. Les principaux résultats d'approximation sont étendus. Nous développons ensuite un cadre théorique pour définir l'homogénéité de systèmes discontinus et/ou donnés par des inclusions différentielles. Nous montrons que les propriétés bien connues des systèmes homogènes restent vérifiées dans ce contexte. Ce travail se poursuit par l'étude de la robustesse des systèmes homogènes ou homogénéisables. Nous montrons que sous des hypothèses peu restrictives, ces systèmes sont input-to-state stable. Enfin, la dernière partie de ce travail consiste en l'étude du cas particulier du double intégrateur. Nous développons pour ce système un retour de sortie qui le stabilise en temps fini, et pour lequel nous prouvons des propriétés de robustesse par rapport à des perturbations ou à la discrétisation en exploitant les résultats développés précédemment. Des simulations viennent compléter l'étude théorique de ce système et illustrer son comportement The purpose of this work is the study of stability and robustness properties of nonlinear systems using homogeneity-based methods. Firstly, we recall the usual context of homogeneous systems as well as their main features. The sequel of this work extends the homogenization of nonlinear systems, which was already defined in the framework of weighted homogeneity, to the more general setting of the geometric homogeneity. The main approximation results are extended. Then we develop a theoretical framework for defining homogeneity of discontinuous systems and/or systems given by a differential inclusion. We show that the well-known properties of homogeneous systems persist in this context. This work is continued by a study of the robustness properties of homogeneous or homogenizable systems. We show that under mild assumptions, these systems are input-to-state stable. Finally, the last part of this work consists in the study of the example of the double integrator system. We synthesize a finite-time stabilizing output feedback, which is shown to be robust with respect to perturbations or discretization by using techniques developed before. Simulations conclude the theoretical study of this system and illustrate its behavior

APA, Harvard, Vancouver, ISO, and other styles

16

GUTIERREZ, Alex Neri. "Um método de averaging para inclusoes diferenciais fuzzy." Universidade Federal de Goiás, 2012. http://repositorio.bc.ufg.br/tede/handle/tde/1954.

Full text

Abstract:

Made available in DSpace on 2014-07-29T16:02:20Z (GMT). No. of bitstreams: 1 ALEX NERI GUTIERREZ DISSERTACAO.pdf: 1234288 bytes, checksum: ae65a58b7c2fd793b3c15d44001d82d6 (MD5) Previous issue date: 2012-03-23 This work has the main objective in the context of the fuzzy theory. Averaging method, differential inclusions are studied; finally this context of the fuzzy theory. O trabalho tem como objetivo principal, o estudo de um método de averaging em problemas de valor inicial no contexto fuzzy. Com o intuito de facilitar a compreensão do trabalho, faz-se um estudo do, um método de averaging no contexto determinístico, teoria de inclusões diferencias, teoria dos conjuntos fuzzy, inclusões diferenciais fuzzy e finalmente mostra-se o um resultado da validade do método de averaging no contexto fuzzy.

APA, Harvard, Vancouver, ISO, and other styles

17

Nguyen, Bao tran. "Contribution à la stabilité de Lyapunov non-régulière des inclusions différentielles avec opérateurs monotones maximaux." Thesis, Limoges, 2017. http://www.theses.fr/2017LIMO0062/document.

Full text

Abstract:

Dans cette thèse de doctorat, nous apportons quelques contributions à la stabilité de Lyapunov non-régulière des inclusions différentielles de premier ordre avec opérateurs monotones maximaux, dans un cadre Hilbertien de dimension infini. Nous fournissons des caractérisations explicites, primales et/ou duales, des paires de Lyapunov faibles et fortes, dont les fonctions sont semi-continues inférieurement à valeurs réelles étendues, et associées à des inclusions différentielles dont la partie de droite est gouvernée par des perturbations Lipschitziennes des opérateurs dits Cusco F, ou des opérateurs monotones maximaux A, ou les deux à la fois x(t) ∈ F(x(t}} A(x(t}} t ≥ 0, x(0) ∈ domA. De manière équivalente, nous étudions l'invariance faible et forte des ensembles fermés pour ces inclusions différentielles. Comme dans L'approche classique de Lyapunov à la stabilité des équations différentielles, les résultats présentés dans cette thèse n'utilisent que les données du système différentiel; c'est-à-dire, l'opérateur A et la multifonction F, et donc pas besoin de connaître les solutions, ni les semi-groupes générés par les opérateurs monotones en question. Parce que les paires de Lyapunov sont formées par des fonctions qui sont simplement semi-continues inférieurement, et les ensembles invariants ne sont que ensembles fermés, nous faisons usage dans cette thèse à des outils de l'analyse non-lisse, afin de fournir des critères du premier ordre, utilisant des sous-différentiels généraux et des cônes normaux. Nous fournissons une analyse similaire pour les inclusions différentielles gouvernées par le cône normal proximal à des ensembles prox-réguliers. Notre analyse ci-dessus, nous a permis de présenter ces systèmes prox-réguliers d’apparence plus générale, comme des inclusions différentielles avec opérateurs monotones maximaux. Nous utilisons aussi nos résultats pour étudier la géométrie des opérateurs monotones maximaux, et plus précisément, la caractérisation de la frontière des valeurs de ces opérateurs seulement au moyen des valeurs situées à proximité, distinctes du point de référence. Ce résultat a des applications dans la stabilité des problèmes de la programmation semi-infinie. Nous utilisons également nos résultats sur les paires de Lyapunov et les ensembles invariants pour établir une étude systématique des observateurs de type Luenberger pour des inclusions différentielles avec des cônes normaux à des ensembles prox-réguliers In this PhD thesis, we make some contributions to nonsmooth Lyapunov stability of first-order differential inclusions with maximal monotone operators, in the setting of infinite-dimensional Hilbert spaces. We provide primal and dual explicit characterizations for parameterized weak and strong Lyapunov pairs of lower semicontinuous extended-real-valued functions, referred to as a-Lyapunov pairs, associated to differential inclusions with right-hand-sides governed by Lipschitz or Cusco perturbationsF of maximal monotone operators A, x(t) ∈ F(x(t}} A(x(t}} t ≥ 0, x(0) ∈ domA. Equivalently, we study the weak and strong invariance of sets with respect to such differential inclusions. As in the classical Lyapunov approach to the stability of differential equations, the presented results make use of only the data of the differential system; that is, the operator A and the multifunction F, and so no need to know about the solutions, nor the semi-groups generated by the monotone operators. Because our Lyapunov pairs and invariant sets candidates are just lower semicontinuous and closed, respectively, we make use of nonsmooth analysis to provide first-order-like criteria using general subdifferentials and normal cones. We provide similar analysis to non-convex differential inclusions governed by proximal normal cones to prox-regular sets. Our analysis above allowed to prove that such apparently more general systems can be easily coined into our convex setting. We also use our results to study the geometry of maximal monotone operators, and specifically, the characterization of the boundary of the values of such operators by means only of the values at nearby points, which are distinct of the reference point. This result has its application in the stability of semi-infinite programming problems. We also use our results on Lyapunov pairs and invariant sets to provide a systematic study of Luenberger-like observers design for differential inclusions with normal cones to prox-regular sets

APA, Harvard, Vancouver, ISO, and other styles

18

Hamlat, Bastien. "Modélisation mathématique de réactions cinétiques multiphasiques en géochimie." Thesis, Rennes 1, 2020. http://www.theses.fr/2020REN1S013.

Full text

Abstract:

Cette thèse concerne la modélisation mathématique des réactions cinétiques comprenant des phases pures. Dans le premier chapitre, un modèle de type EDOs discontinues pour la cinétique avec apparitions et disparitions d'espèces pour un nombre quelconque de minéraux est proposé. Une version régularisée du modèle permet de prouver la positivité et l’existence. Une analyse explicite plus approfondie dans le cas contenant une espèce réactive intermédiaire est menée. Dans le deuxième chapitre, une reformulation du modèle de cinétique chimique utilisant la théorie de Filippov est proposée. Une preuve de l'existence et de la positivité des solutions est réalisée. De plus, dans le cas des surfaces de discontinuité de codimension 1, une étude des configurations des champs fournit un résultat d'unicité et de caractérisation des trajectoires. Dans le troisième chapitre, un modèle de cinétique chimique de type systèmes dynamiques projetés est proposé. Une analyse de l'existence des solutions de ce modèle, des liens avec d'autres types de formulations et une méthode de résolution numérique adaptée sont proposés. Enfin, une illustration des résultats numériques obtenus est réalisée pour des systèmes de cinétique chimique This thesis focuses on the modeling chemical kinetics for reactions involving pure phases. In the first chapter, a discontinuous ODEs model for reactions with appearance and disappearance of species for any number of minerals is proposed. A regularized version of the model can prove positivity and existence. An explicit analysis in the case containing an intermediate reactive species is investigated. In the second chapter, a reformulation of the chemical kinetics model using Filippov's theory is proposed. A proof of the existence and the positivity of the solutions is given. In addition, in the case of discontinuity surfaces of codimension 1, a study of the configurations of the vector fields provides a result of uniqueness and a characterization of the trajectories. In the third chapter, a model of chemical kinetics of the projected dynamical system is proposed. An analysis of the existence of solutions of this model, links with other types of formulations and an adapted numerical resolution method are provided. An illustration of the numerical results obtained is made for chemical kinetic systems

APA, Harvard, Vancouver, ISO, and other styles

19

Bauwe, Anne, and Wilfried Grecksch. "A parabolic stochastic differential inclusion." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501221.

Full text

Abstract:

Stochastic differential inclusions can be considered as a generalisation of stochastic differential equations. In particular a multivalued mapping describes the set of equations, in which a solution has to be found. This paper presents an existence result for a special parabolic stochastic inclusion. The proof is based on the method of upper and lower solutions. In the deterministic case this method was effectively introduced by S. Carl.

APA, Harvard, Vancouver, ISO, and other styles

20

El, Bachari Rachid. "Contribution à l'étude des algorithmes proximaux : décomposition et perturbation variationnelle." Rouen, 1996. http://www.theses.fr/1996ROUES026.

Full text

Abstract:

Cette thèse est consacrée à la résolution d'inclusions monotones et en particulier de problèmes d'optimisation convexe. D'une part, nous proposons une nouvelle méthode fondée sur une relaxation de l'étape proximale de la méthode de l'inverse partiel ; les tests numériques ont confirmé une amélioration très nette de la vitesse de convergence dans certains cas par rapport aux algorithmes connus. D'autre part, nous proposons une version diagonale de la méthode de Lions-Mercier, ce qui permet notamment en optimisation convexe, de combiner la méthode des directions alternées des multiplicateurs avec une classe importante de méthodes de pénalité.

APA, Harvard, Vancouver, ISO, and other styles

21

Mansouri, Asma. "Exponentiation of set-valued maps and applications." Thesis, Perpignan, 2020. http://www.theses.fr/2020PERP0002.

Full text

Abstract:

Dans cette thèse, nous avons présenté notre contribution au calcul des points fixes pour des équations linéaires et non linéaires. nous avons introduit une nouvelle méthode pour calculer les points fixes d'une classe de fonctions itérées dans un temps fini, en calculant l'exponentiel des opérateurs linéaires multivalués. Afin d'illustrer notre approche et montrer que cette méthode peut donner des résultats rapides et précis pour les équations linéaires et non linéaires, nous avons choisi deux applications bien connues qui sont difficiles à manipuler par les techniques habituelles, pour le cas des équations linéaires. Premièrement, nous appliquons l'exponentiation des opérateurs linéaires à un filtre numérique afin d'obtenir une approximation fine de son comportement à un moment arbitraire. Deuxièmement, on considére un contrôleur PID. Afin d'obtenir une estimation fiable de sa fonction de contrôle, on applique l'exponentiation d'un faisceau d'opérateurs linéaires. Pour le cas des équations non linéaires, nous avons choisi un système dynamique non linéaire, plus précisément un contrôleur en boucle ouverte, et nous avons calculé le point fixe de son approximation linéaire. Notons que cette technique peut être appliquée dans un cadre plus général, pour toute fonction multivoque linéaire et non linéaire et que l'algorithme général est également introduit dans ce manuscrit In this thesis, we presented our contribution to the computation of fixed-points for both linear and nonlinear equations. We introduced a new method for computing fixed points of a class of iterated functions in a finite time, by exponentiating linear multivalued operators. In order to illustrate our approach and show that this method can give fast and accurate results for both linear and non linear equations, we have chosen two well-known applications which are difficult to handle by usual techniques, for linear equations case. First, we apply the exponentiation of linear operators to a digital filter in order to get a fine approximation of its behavior at an arbitrary time. Second, we consider a PID controller. In order to get a reliable estimate of its control function, we apply the exponentiation of a bundle of linear operators. For the non linear equations case, we have chosen a dynamic non linear system, more precisely, an open loop control command system, and we computed the fixed point of its linear approximation. Note that, this technique can be applied in a more general setting, for any multivalued linear and non linear map and that the general algorithm is also introduced in this manuscript

APA, Harvard, Vancouver, ISO, and other styles

22

Maulen, Soto Rodrigo. "A dynamical system perspective οn stοchastic and iΙnertial methοds fοr optimizatiοn". Electronic Thesis or Diss., Normandie, 2024. http://www.theses.fr/2024NORMC220.

Full text

Abstract:

Motivé par l'omniprésence de l'optimisation dans de nombreux domaines de la science et de l'ingénierie, en particulier dans la science des données, ce manuscrit de thèse exploite le lien étroit entre les systèmes dynamiques dissipatifs à temps continu et les algorithmes d'optimisation pour fournir une analyse systématique du comportement global et local de plusieurs systèmes du premier et du second ordre, en se concentrant sur le cadre convexe, stochastique et en dimension infinie d'une part, et le cadre non convexe, déterministe et en dimension finie d'autre part. Pour les problèmes de minimisation convexe stochastique dans des espaces de Hilbert réels séparables de dimension infinie, notre proposition clé est de les analyser à travers le prisme des équations différentielles stochastiques (EDS) et des inclusions différentielles stochastiques (IDS), ainsi que de leurs variantes inertielles. Nous considérons d'abord les problèmes convexes différentiables lisses et les EDS du premier ordre, en démontrant une convergence faible presque sûre vers les minimiseurs sous hypothèse d'intégrabilité du bruit et en fournissant une analyse globale et locale complète de la complexité. Nous étudions également des problèmes convexes non lisses composites utilisant des IDS du premier ordre et montrons que, sous des conditions d'intégrabilité du bruit, la convergence faible presque sûre des trajectoires vers les minimiseurs, et avec la régularisation de Tikhonov la convergence forte presque sûre des trajectoires vers la solution de norme minimale. Nous développons ensuite un cadre mathématique unifié pour analyser la dynamique inertielle stochastique du second ordre via la reparamétrisation temporelle et le moyennage de la dynamique stochastique du premier ordre, ce qui permet d'obtenir une convergence faible presque sûre des trajectoires vers les minimiseurs et une convergence rapide des valeurs et des gradients. Ces résultats sont étendus à des EDS plus générales du second ordre avec un amortissement visqueux et Hessien, en utilisant une analyse de Lyapunov spécifique pour prouver la convergence et établir de nouveaux taux de convergence. Enfin, nous étudions des problèmes d'optimisation déterministes non convexes et proposons plusieurs algorithmes inertiels pour les résoudre, dérivés d'équations différentielles ordinaires (EDO) du second ordre combinant à la fois un amortissement visqueux sans vanité et un amortissement géométrique piloté par le Hessien, sous des formes explicites et implicites. Nous prouvons d'abord la convergence des trajectoires en temps continu des EDO vers un point critique pour des objectives vérifiant la propriété de Kurdyka-Lojasiewicz (KL) avec des taux explicites, et génériquement vers un minimum local si l'objective est Morse. De plus, nous proposons des schémas algorithmiques par une discrétisation appropriée de ces EDO et montrons que toutes les propriétés précédentes des trajectoires en temps continu sont toujours valables dans le cadre discret sous réserve d'un choix approprié de la taille du pas Motivated by the ubiquity of optimization in many areas of science and engineering, particularly in data science, this thesis exploits the close link between continuous-time dissipative dynamical systems and optimization algorithms to provide a systematic analysis of the global and local behavior of several first- and second-order systems, focusing on convex, stochastic, and infinite-dimensional settings on the one hand, and non-convex, deterministic, and finite-dimensional settings on the other hand. For stochastic convex minimization problems in infinite-dimensional separable real Hilbert spaces, our key proposal is to analyze them through the lens of stochastic differential equations (SDEs) and inclusions (SDIs), as well as their inertial variants. We first consider smooth differentiable convex problems and first-order SDEs, demonstrating almost sure weak convergence towards minimizers under integrability of the noise and providing a comprehensive global and local complexity analysis. We also study composite non-smooth convex problems using first-order SDIs, and show under integrability conditions on the noise, almost sure weak convergence of the trajectory towards a minimizer, with Tikhonov regularization almost sure strong convergence of trajectory to the minimal norm solution. We then turn to developing a unified mathematical framework for analyzing second-order stochastic inertial dynamics via time scaling and averaging of stochastic first-order dynamics, achieving almost sure weak convergence of trajectories towards minimizers and fast convergence of values and gradients. These results are extended to more general second-order SDEs with viscous and Hessian-driven damping, utilizing a dedicated Lyapunov analysis to prove convergence and establish new convergence rates. Finally, we study deterministic non-convex optimization problems and propose several inertial algorithms to solve them derived from second-order ordinary differential equations (ODEs) combining both non-vanishing viscous damping and geometric Hessian-driven damping in explicit and implicit forms. We first prove convergence of the continuous-time trajectories of the ODEs to a critical point under the Kurdyka-Lojasiewicz (KL) property with explicit rates, and generically to a local minimum under a Morse condition. Moreover, we propose algorithmic schemes by appropriate discretization of these ODEs and show that all previous properties of the continuous-time trajectories still hold in the discrete setting under a proper choice of the stepsize

APA, Harvard, Vancouver, ISO, and other styles

23

Latreche, Wissam. "Some aspects on sweeping processes." Thesis, Perpignan, 2018. http://www.theses.fr/2018PERP0011/document.

Full text

Abstract:

Dans cette thèse, on s'intéresse à l'étude d'existence de solutions pour les processus de rafle. Ce problème prend la forme d'une inclusion différentielle contrainte avec des cônes normaux qui apparaissent naturellement dans nombreuses applications telles que le mouvement de foule, l'élastoplasticité, les mécaniques, les circuits électroniques, etc. L'objective de ce travail est de rapprocher deux importantes classes d'inclusions différentielles. D'une part, nous établissons quelques résultats d'existence de tube-solutions pour des processus de rafle à des ensembles uniformément prox-réguliers. D'autre part, nous présentons des résultats d'existence de solutions monotone par rapport à un préordre pour un système mixte d'inclusions différentielles projetées. De plus, nous montrons l'existence d'un point-selle pour notre système et nous fournissons deux exemples d'applications In this thesis, we were interested in the study of the existence of solutions for sweeping processes. This problem takes the form of a constrained differential inclusion involving normal cones which appears naturally in many applications such as crowd motion, elastoplasticity, mechanics, electrical circuit, etc.The aim of this work is to bring together two classes of differential inclusions. On one hand, we establish some existence results of solutions-tube for sweeping processes with uniformly prox-regular sets. On the other hand, we present existence results of monotone solutions with respect to a preorder for a mixed system of projected differential inclusions. In addition, we show that our system has a saddle-point and we provide two examples of applications

APA, Harvard, Vancouver, ISO, and other styles

24

Clérin, Jean-Marc. "Problèmes de contrôle optimal du type bilinéaire gouvernés par des équations aux dérivées partielles d’évolution." Thesis, Avignon, 2009. http://www.theses.fr/2009AVIG0405/document.

Full text

Abstract:

Cette thèse est une contribution à l’étude de problèmes de contrôle optimal dont le caractère non linéaire se traduit par la présence, dans les équations d’état, d’un terme bilinéaire relativement à l’état et au contrôle. Malgré les difficultés liées à la non linéarité, nous obtenons des propriétés spécifiques au cas bilinéaire. L’introduction générale constitue la première partie. La seconde partie est consacrée à l’étude des équations d’état ; ce sont des équations aux dérivées partielles d’évolution. Nous établissons des estimations a priori sur les solutions à partir des inégalités de Willett et Wong et nous démontrons que les équations d’états sont bien posées. Dans le cas où les contrôles subissent une contrainte liée aux états, ces estimations permettent de déduire l’existence de solutions dans le cadre des inclusions différentielles. Les troisième et quatrième parties de ce mémoire sont dévolues à la démonstration de l’existence de contrôles optimaux, puis à l’analyse de la sensibilité relative à une perturbation qui intervient de façon additive dans l’équation d’état. Le caractère bilinéaire permet de vérifier des conditions suffisantes d’optimalité du second ordre. Nous fournissons sur des exemples, une formule explicite des dérivées directionnelles de la fonction valeur optimale This thesis is devoted to the analysis of nonlinear optimal control problems governed by an evolution state equation involving a term which is bilinear in state and control. The difficulties due to nonlinearity remain, but bilinearity adds a lot of structure to the control problem under consideration. In Section 2, by using Willet and Wong inequalities we establish a priori estimates for the solutions of the state equation. These estimates allow us to prove that the state equation is well posed in the sense of Hadamard. In the case of a feedback constraint on the control, the state equation becomes a differential inclusion. Under mild assumptions, such a differential inclusion is solvable. In Section 3, we prove the existence of solutions to the optimal control problem. Section 4 is devoted to the sensitivity analysis of the optimal control problem. We obtain a formula for the directional derivative of the optimal value function. This general formula is worked out in detail for particular examples

APA, Harvard, Vancouver, ISO, and other styles

25

Mu, Wangzhong. "Microstructure and Inclusion Characteristics in Steels with Ti-oxide and TiN Additions." Doctoral thesis, KTH, Tillämpad processmetallurgi, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-162284.

Full text

Abstract:

Non-metallic inclusions in steels are generally considered to be detrimental for mechanical properties. However, it has been recognized that certain inclusions, such as Ti-oxide and TiN, can serve as potent nucleation sites for the formation of intragranular ferrite (IGF) in low-alloy steels. The formation of IGF could improve the toughness of the coarse grained heat affected zone (CGHAZ) of weld metals. Thus, the present thesis mainly focuses on the effect of size of nucleation sites on the IGF formation. Quantitative studies on the composition, size distribution and nucleation probability for each size of the inclusions as well as the area fraction, starting temperature and morphology of an IGF have been carried out. In the present work, the Ti-oxide and TiN powders were mixed with metallic powders. The mixed powders were heated up to the liquid state and cooled with a slow cooling rate of 3.6 ºC/min. These as-cast steels with Ti-oxide and TiN additions were used to simulate the IGF formation in the CGHAZ of weld metals. Specifically, the inclusion and microstructure characteristics in as-cast steels have been investigated. The results show that the nucleant inclusion was identified as a TiOx+MnS phase in steels with Ti2O3 additions and as a TiN+Mn-Al-Si-Ti-O+MnS phase in steels with TiN additions. In addition, the TiOx and TiN phases are detected to be the effective nucleation sites for IGF formation. It is clearly shown that an increased inclusion size leads to an increased probability of IGF nucleation. This probability of IGF nucleation for each inclusion size of the TiOx+MnS inclusions is clearly higher than that of the complex TiN+Mn-Al-Si-Ti-O+MnS inclusions. In addition, the area fraction of IGF in the steels with Ti2O3 additions is larger than that of the steels with TiN additions. This result agrees with the predicted tendency of the probability of IGF nucleation for each inclusion size in the steels with Ti2O3 and TiN additions. In order to predict the effective inclusion size for IGF formation, the critical diameters of the TiO, TiN and VN inclusions, which acted as the nucleation sites of IGF formation, were also calculated based on the classical nucleation theory. The critical diameters of TiO, TiN and VN inclusions for IGF formation were found to be 0.192, 0.355 and 0.810 μm in the present steels. The calculation results were found to be in agreement with the experiment data of an effective inclusion size. Moreover, the effects of the S, Mn and C contents on the critical diameters of inclusions were also calculated. It was found that the critical diameter of the TiO, TiN and VN inclusions increases with an increased content of Mn or C. However, the S content doesn’t have a direct effect on the critical diameter of the inclusions for IGF formation. The probability of IGF nucleation for each inclusion size slightly decreases in the steel containing a higher S content. This fact is due to that an increased amount of MnS precipitation covers the nucleant inclusion surface. In the as-cast experiment, it was noted that an IGF can be formed in steels with Ti2O3 and TiN additions with a cooling rate of 3.6 ºC/min. In order to control the microstructure characteristics, such as the area fraction and the morphology of an IGF, and to investigate the starting temperature of IGF and grain boundary ferrite (GBF) formation, the dynamic transformation behavior of IGF and GBF was studied in-situ by a high temperature confocal laser scanning microscope (CLSM). Furthermore, the chemical compositions of the inclusions and the morphology of IGF after the in-situ observations were investigated by using scanning electron microscopy (SEM), electron backscatter diffraction (EBSD) and electron probe microanalysis (EPMA) which equipped wavelength dispersive spectrometer (WDS). The results show that the area fraction of IGF is larger in the steels with Ti2O3 additions compared to the steels with TiN additions, after the same thermal cycle has been imposed. This is due to that the TiOx phase provides more potent nucleation sites for IGF than the TiN phase does. Also, the area fraction of IGF in the steels is highest after at an intermediate cooling rate of 70 ºC/min, since the competing phase transformations are avoided. This fact has been detected by using a hybrid methodology in combination with CLSM and differential scanning calorimetry (DSC). In addition, it is noted that the morphology of an IGF is refined with an increased cooling rate. QC 20150325

APA, Harvard, Vancouver, ISO, and other styles

26

Fabini, G. "BORDERING SUBJECTS. THE UNSPOKEN INCORPORATION OF UNDOCUMENTED MIGRANTS IN ITALY." Doctoral thesis, Università degli Studi di Milano, 2016. http://hdl.handle.net/2434/362930.

Full text

Abstract:

Socio-legal and criminological research make sense of the mechanisms of border control by taking for granted that the main aim of logic of control is one to exclude, therefore they generally focus on removal procedures. My research takes a different approach: my focus is on the far more frequent conditions under which undocumented migrants are informally allowed to remain despite official permission. Therefore, in looking at the immigration control regimes, my focus will be on undocumented migrants living inside national territories rather than removal procedures. Undocumented migrants are generally seen as resulting from immigration law failing to enforce removal. On the contrary, I argue that undocumented migrants living inside national territories may be seen as the very product of law instead of its failure. In a sense, immigration control regimes are mechanisms that exclude through removal and at the same time processes of production of a new subject, that is, the undocumented migrant living inside national territories despite official permission. This thesis aims to enrich the literature on control by looking at the differential inclusion of those many undocumented migrants living in the territory. Differential inclusion is a concept elaborated by Sandro Mezzadra and Brett Neilson (2013); it is an invitation to look at the mechanisms of inclusion that can involve various degrees of subordination, rule, discrimination, racism, disenfranchisement, exploitation and segmentation. In this line, the foucauldian concept of discipline goes exactly in the direction of acknowledging punishment, specifically imprisonment, as a tool to normalize individuals, in order to make them to conform to the norm and include them in disciplined societies (Foucault, 1977). Hence, inclusion and exclusion are assembled logics. As well as it seems a logic of inclusion the one behind imprisonment, at least at the origin of capitalism and the modern state: prison is aimed at disciplining the individual to labour, at producing the disciplined worker useful for the development of capitalistic economy (Melossi and Pavarini, 1981). My theoretical perspective will move from here. One main concern of the present work is that, even if internal border control relies on similar discourses, power relations, and laws at the global level, I argue that it produce dissimilar outcomes depending on the local context. Therefore, by accepting Saskia Sassen’s invitation to see “the global inside the national” (Sassen, 2010), my aim is to show that the global logics meet other logics, conditions, and history at the local level, which affects the expected outcomes. On the one hand, the outcomes of global borders control depend on the local level; on the other hand, the local dimension is the only dimension where it is possible to study, recognize and understand even global dynamics. Using a case study of internal border control in Bologna, Italy, I will examine the logics underpinning global border control at the local level, as this may question the logics of global border control often taken for granted. The core of investigation will be the interaction between police and undocumented migrants at the internal borders, that is, once migrants have crossed external borders and live inside the territory. My case study looks at undocumented migrants in Bologna (Italy) continually undergoing police checks, being charged, and even detained. Few are actually removed; the great majority remains and finds their place in the Italian shadow economy. I argue that what we see in Bologna is a logic of subordinated inclusion rather than exclusion, whose main result is the production of a subject who may not completely belong, yet is not completely excluded either. Police are at the core of present investigation, as the Italian immigration law entrusts the control over undocumented immigration to general police (a specific immigration police have never been issued in Italy indeed). Even so, police practices are not taken into consideration alone: what really stands at the core of present research is the interaction between migrants and police. I consider that migrants are not passive subjects in the immigration control regime, but by enacting strategies of resistance, they oppose the police, force them towards negotiation, and contribute to the final results of interaction. The present analysis acknowledges that migrants oppose strategies of subjectivation to the strategies of subjection enacted by the police, which originates that migrants are active agents in the mechanisms of control that produce them as subjects. The conclusions discuss the importance to broaden our consideration of the elements taking part in the immigration control regime. They proposes that immigration penalty is much wider than just removal procedures. They summarize the process of creation of the peculiar subject of the present case study, underling global and local dynamics of power, and it will shed light on the connection between penalty, border, and economy. The process of bordering subjects in the specific case study of this investigation opens up for two additional considerations. 1 the analysis of border control should also take economy into account. 2) the bodies of undocumented migrants are the concrete manifestation of the link between economy and penalty. I argue that the complex processes through which undocumented migrants are produced as subject may be analysed as one segment of “the discursive interactions of all the actors“ (Melossi 2008: 7) which link penalty and economy. The research is aimed at answering the crucial question of how such mechanisms come to be. In fact, rather than as a well-organized and preconceived apparatus, the mechanisms of control is intended as the result of not planned actions of individual actors, who time after time look for the “best” way to manage the complex situation of undocumented immigration.

APA, Harvard, Vancouver, ISO, and other styles

27

Nguyen, Vo Anh Thuong. "Mathematical and numerical modeling on the Sweeping process : applications to contact dynamics." Electronic Thesis or Diss., Perpignan, 2024. http://www.theses.fr/2024PERP0022.

Full text

Abstract:

Basé sur l'importance croissante de comprendre les médias granulaires et leurs comportements dans diverses industries, ce travail propose une nouvelle méthode différente de la Méthode des Éléments Discrets (Discrete Element Method-DEM) et de l'approche de la Dynamique de Contact Non Lisse (Non-Smooth Contact Dynamics-NSCD) pour modéliser la dynamique granulaire. Nous nous concentrons sur un processus de balayage discontinu de Moreau de second ordre pour modéliser la dynamique de contact, en incorporant la régularisation de Moreau-Yosida avec le paramètre ( alpha ) pour développer un modèle de contact régulier. Nous proposons la méthode textbf{Improved Normal Compliance} (INC) pour assurer la conservation de l'énergie et employons une combinaison de la méthode de Newmark et de textbf{Primal-Dual Active Set} (PDAS) pour traiter la non-linéarité. Cette étude vise à comparer l'efficacité de notre approche avec d'autres techniques de modélisation numérique, telles que DEM et NSCD via la méthode de Gauss-Seidel Non Linéaire (Nonlinear Gauss Seidel method-NLGS), en se concentrant sur l'amélioration de la conservation de l'énergie et du coût computationnel. En outre, en relation avec le processus de balayage de Moreau, pour établir l'existence d'une solution, il est assez naturel d'aller au-delà de la convexité avec la prox-régularité ou la classe duale associée à l'ensemble prox-régulier qui est un ensemble fortement convexe. De plus, la régularité métrique sert d'outil utile pour étudier la faible convexité de sous-ensembles spécifiques. Plus précisément, nous nous concentrerons sur deux idées principales. Premièrement, nous considérons les concepts de textbf{Fonction de distance la plus éloignée aux ensembles fortement convexes dans les espaces de Hilbert}. D'une part, nous montrons que la forte convexité d'un ensemble est équivalente à la semi-concavité de sa fonction de distance la plus éloignée associée. D'autre part, nous établissons que la distance la plus éloignée d'un point à un ensemble fortement convexe est la distance la plus éloignée minimale au point donné à partir de boules fermées appropriées séparant l'ensemble et le point. Deuxièmement, nous nous concentrons sur textbf{la sous-régularité métrique et les propriétés de régularité omega cdot) -normales}. Nous établissons par une condition d'ouverture la sous-régularité métrique d'une multi-application avec la régularité omega cdot) -normale soit du graphe, soit des valeurs. Divers résultats de préservation pour les ensembles prox-réguliers et sous-lisses sont également fournis Based on the growing importance of understanding granular media and their behaviors in various industries, this work proposes a new method different from the Discrete Element Method (DEM) and the Non-Smooth Contact Dynamics (NSCD) approach to model granular dynamics. We focus on a discontinuous Moreau second-order sweeping process for modeling contact dynamics, incorporating the Moreau-Yosida regularization with parameter alpha to develop a regular contact model. We propose the textbf{Improved Normal Compliance} (INC) method to ensure energy conservation and employ a combination of the Newmark method and textbf{Primal-Dual Active Set} (PDAS) to address nonlinearity. This study aims to compare the efficiency of our approach with other numerical modeling techniques, such as DEM and NSCD via Nonlinear Gauss Seidel method (NLGS), focusing on improving energy conservation and computational cost. Furthermore, related to the Moreau sweeping process, to establish the existence of a solution, it is quite natural to extend beyond convexity with prox-regularity or the dual class associated with the prox-regular set, which is a strongly convex set. Additionally, metric regularity serves as a useful tool for studying the weak convexity of specific subsets. More precisely, we will focus on two main ideas. First, we consider the concepts of textbf{Farthest distance function to strongly convex sets in Hilbert spaces}. On one hand, we show that the strong convexity of a set is equivalent to the semiconcavity of its associated farthest distance function. On the other hand, we establish that the farthest distance of a point to a strongly convex set is the minimum farthest distance to the given point from suitable closed balls separating the set and the point. Second, we concentrate on textbf{Metric subregularity and omega cdot)-normal regularity properties}. We establish through an openness condition the metric subregularity of a multimapping with normal omega cdot) -regularity of either the graph or values. Various preservation results for prox-regular and subsmooth sets are also provided

APA, Harvard, Vancouver, ISO, and other styles

28

Chá, Sílvia Alexandra Carrapato. "Problemas convexos e não-convexos do cálculo das variações." Doctoral thesis, Universidade de Évora, 2014. http://hdl.handle.net/10174/17929.

Full text

Abstract:

Nas aplicações do Cálculo das Variações, Controlo Óptimo & Inclusões Diferenciais, muitos problemas importantes da vida real são vectoriais não-convexos e sujeitos a restrições pontuais. O teorema clássico da convexidade de Liapunov é uma ferramenta crucial para resolver problemas vectoriais não-convexos envolvendo integrais simples. No entanto, a possibilidade da extensão deste teorema para lidar com restrições pontuais manteve-se um problema em aberto durante duas décadas, no caso mais realista usando controlos vectoriais variáveis. Nesta tese apresentamos condições necessárias e condições suficientes para a resolução deste problema; CONVEX AND NONCONVEX PROBLEMS OF THE CALCULUS OF VARIATIONS Abstract In applications of the Calculus of Variations, Optimal Control & Differential Inclusions, very important real-life problems are nonconvex vectorial and subject to pointwise constraints. The classical Liapunov convexity theorem is a crucial tool allowing researchers to solve nonconvex vectorial problems involving single integrals. However, the possibility of extending such theorem so as to deal with pointwise constraints has remained an open problem for two decades, in the more realistic case using variable vectorial controls. In this thesis we present necessary conditions and sufficient conditions for solvability of such problem.

APA, Harvard, Vancouver, ISO, and other styles

29

Johan, Filip Rindler Johan Filip. "Lower Semicontinuity and Young Measures for Integral Functionals with Linear Growth." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:c4736fa2-ab51-4cb7-b1d9-cbab0ede274b.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Huber, Olivier. "Analyse et implémentation du contrôle par modes glissants en temps discret." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAT042.

Full text

Abstract:

Le contrôle par mode glissant est une technique d'automatique qui possède une longue histoire, la littérature remontant jusqu'au année 50. Son essence est la suivante : le contrôle est définit comme étant l'image d'une fonction discontinue de la variable de glissement, contraignant le système à évolué sur une variété, le système glisse alors dessus, d'où le nom. Cette variable de glissement est elle définie à partir de l'état du système. Les développements ont mené à la constitution d'une théorie bien établie à propos de cette technique, avec de nombreuses propriétés théoriques fort intéressante. Toutefois ceci ne porte que sur la version continue, c'est à dire quand le contrôle peut changer de valeur à chaque instant. En comparaison la version discrète du ce contrôleur est définie par le fait que la valeur du contrôle ne peut changer qu'à des instants isolés discrets. On a alors une fonction en escalier, constante sur la période d'échantillonnage. Cette situation est rencontrée par exemple lorsque le contrôleur est implémenté à l'aide d'un micro-contrôleur, ce qui est le cas dans nombre d'applications industrielles. Le principal problème avec le mode glissant est l'apparition d'un phénomène largement indésirable, le chattering (ou broutement) avec la version discrète du contrôleur, où même déjà en simulation. Dans ce dernier cas, nous appelons ceci du chattering numérique que nous attribuons à une mauvaise discrétisation du contrôle. L'approche développée ici se focalise sur ce point et est largement inspirée par les travaux effectués en mécanique non régulière, où ce type de comportement a aussi été observé lors de la simulation de système avec frottements et/où impacts. L'idée principale est de discretisé le contrôle de manière implicite et non explicite. Ceci permet d'éliminer le chattering numérique dans les cas simples (systèmes linéaires par exemple) où bien de le réduire grandement. Pour mener à bien l'analyse, des outils provenant de l'analyse convexe ainsi que des inégalités variationnelles en dimension finie sont utilisés. Le contrôleur proposé possède des propriétés intéressantes et proches de celles du temps continu. Ainsi on peut montrer que la variable de glissement est régie par une dynamique stable en temps finie, avec une fonction de Lyapunov. Le contrôle discret convergence vers celui du cas continu quand la période d'échantillonnage tends vers 0. Une atténuation d'éventuelles perturbations de type "matching" peut être établie. Ces travaux ont essentiellement portés sur le contrôle par mode glissant classique. L'algorithme dit twisting a pu être discrétisé avec la même technique et sa stabilité en temps finie grâce à une fonction de Lyapunov a pu être montrée. Ces propriétés ont été vérifiée en simulation, mais aussi de manière expérimentale. Ainsi des essais ont pu être menés sur deux banc d'essai: le premier est basé sur un système electropneumatique où à la fois le contrôle par mode glissant classique ainsi que le twisting ont pu être implémentés. L'objectif étant de suivre une trajectoire de référence. Le second système est un pendule inverse où le système doit être stabilisé à la position d'équilibre instable. Ici seul le contrôleur classique a été testé. L'analyse des données expérimentales a permis de mettre en lumière les performances supérieures des contrôleurs proposés par rapport à ceux classiquement usités. Les objectifs de contrôle sont mieux atteint et le chattering est grandement diminué Sliding Mode Control is a control technique with a long history, with research efforts dating back to the 50's. The basic idea is to define the control input as a discontinuous function of the sliding variable, which solely depends on the state, and to constraint the system to evolve on a manifold, hence the term sliding. Over the years a strong theory was build around this technique, but only in continuous time. In our context, this means that control input value can change value at any time. The discrete-time case is when the control input can only change at isolated time instants and the dynamical system on which the control is still a continuous-time process. The control input is therefore a step function. This case appears when the controller is digitally implemented, for instance with the help of a microcontroller. This kind of setup is nowadays ubiquitous in benchmarks and industrial applications. One of the main limitation of the applicability of sliding mode control is the chattering phenomenon that is witnessed when this control technique is applied in practice, but already in simulations. In contrast to previous approaches, we single out the chattering that is already witnessed in simulation, even with no disturbance and with perfect knowledge of the dynamics. This is called the numerical chattering and one of its distinct feature is the constant chattering, or high-frequency bang-bang behavior, of the control input. This naturally induces a chattering of the sliding variable. The claim that this type of chattering is usually predominant and that it is due to a bad discretization of the signum multifunction. The approach developed in this work was inspired by the research effort in the nonsmooth mechanical to properly simulate some systems like those with dry friction and/or unilateral constraints. The main point is to discretize the signum in an implicit fashion, that is its argument is the value of the sliding variable at the end of the next sampling period. With this change, the numerical chattering can be removed in the simplest cases, largely attenuated. The research effort was focused on classical sliding mode controller, rather than the higher order ones. The frameworks used to perform the analysis are convex analysis and variational inequalities. This discrete-time controller enjoys several interesting theoretical properties. First it is finite-time Lyapunov stable: the sliding variable goes to 0 in finite-time. The discrete-time control input converges to the continuous-time one as the sampling period goes to 0. The control action also attenuates the effect of matched perturbations. Also the increase of the gain of the controller does not affect the performances when the system is sliding. The twisting controller can be discretized in the same way and is also finite-time Lyapunov stable. This good theoretical properties have been verified in simulations, but also on experimental setups. Two tests were conducted: the first one on an electropneumatic system, where both the classical first-order sliding mode controller and the twisting algorithm were tested. The objective was to track a reference trajectory. The second one was an inverted pendulum on a cart with only the classical SMC. The goal was to stabilize the system at the unstable equilibrium. The analysis from the data collected during those experiments shows that the proposed controllers perform better than the their explicitly discretized versions. The performances are better and the chattering is effectively reduced

APA, Harvard, Vancouver, ISO, and other styles

31

Hechaichi, Hadjer. "Problèmes de contrôle optimal associés avec des inégalités variationnelles et différentielles variationnelles." Thesis, Perpignan, 2019. http://www.theses.fr/2019PERP0008.

Full text

Abstract:

Les problèmes de contrôle optimal se rencontrent dans l'industrie aérospatiale et dans la mécanique. Leur étude conduit à des difficultés mathématiques importantes. Dans cette thèse, nous nous intéressons aux conditions d'optimalité pour certains problèmes de contrôle avec des contraintes exprimées en termes d'inclusions différentielles. Nous considérons aussi des problèmes de contrôle associés aux modèles mathématiques issus de la Mécanique du Contact. Cette thèse est structurée en deux parties et six chapitres. La première partie, contenant les Chapitres 1, 2 et 3, représente un résumé de nos résultats, en Français. Nous y présentons les problèmes étudiés, les hypothèses sur les données, les notations utilisées ainsi que l’énoncé des principaux résultats. Les démonstrations sont omises. La deuxième partie du manuscrit représente la partie principale de la thèse. Elle contient les Chapitres 4, 5 and 6, chacun ayant fait l'objet d'une publication (parue ou soumise) dans une revue internationale avec comité de lecture.Nous y présentons nos principaux résultats, accompagnés des démonstrations et des références bibliographiques Optimal control problems arise in aerospace industry and in mechanics. They are challenging and involve important mathematical difficulties. In this thesis, we are interested to derive optimality conditions for optimal control problems with constraints under the form of differential inclusions. We also consider optimal control problems in the study of some boundary value problems arising in Contact Mechanics. The thesis is structured in two parts and six chapters. Part I represents an abstract of the main results, in French. It contains Chapters 1, 2 and 3. Here we present the problems we study together with the assumptions on the data, the notation and the statement of the main results. The proofs of these results are omitted, since them are presented in Part II of the manuscript.Part II represents the main part of the thesis. It contains Chapters 4, 5 and 6. Each of these chapters made the object of a paper published (or submitted) in an international journal. Here we present our main results, together with the corresponding proofs and bibliographical references

APA, Harvard, Vancouver, ISO, and other styles

32

Fröhlich, Raquel. "Práticas de apoio à inclusão escolar e a constituição de normalidades diferenciais." Universidade do Vale do Rio dos Sinos, 2018. http://www.repositorio.jesuita.org.br/handle/UNISINOS/6928.

Full text

Abstract:

Submitted by JOSIANE SANTOS DE OLIVEIRA (josianeso) on 2018-03-19T13:35:10Z No. of bitstreams: 1 Raquel Fröhlich_.pdf: 1849961 bytes, checksum: d9c9074d7c6a880f4a344c6865b6002b (MD5) Made available in DSpace on 2018-03-19T13:35:10Z (GMT). No. of bitstreams: 1 Raquel Fröhlich_.pdf: 1849961 bytes, checksum: d9c9074d7c6a880f4a344c6865b6002b (MD5) Previous issue date: 2018-02-22 Nenhuma Esta Tese tem o objetivo de compreender de que maneira as práticas de apoio à inclusão escolar colocam em funcionamento processos de normalização das pessoas com deficiência a partir da década de 1990. Para isso, foram utilizados como material empírico 11 políticas, nacionais e internacionais, que regulamentam práticas de inclusão escolar no Brasil de 1990 até 2015. Os materiais foram analisados utilizando-se a ferramenta da normalização, conforme Michel Foucault. As análises dos documentos mostram práticas de apoio, produzidas e requeridas pelas políticas de inclusão, que objetivam criar as condições para a manutenção dos alunos com deficiência na escola comum. Também mostram a necessária criação dos serviços em rede e circulação dos sujeitos nesses serviços. Cada profissional que compõe a rede de serviços produz um diagnóstico segundo suas competências técnicas com informações que chegam à escola. Na escola, as informações produzem uma individualização das intervenções educativas, com o objetivo de desenvolver aprendizagens. Conclui-se que as práticas de apoio terceirizadas operam com processos de normalização que não apenas visam à correção, mas também fragmentam o sujeito com deficiência, indicando capacidades para a aprendizagem. Defende-se a tese de que as práticas de apoio terceirizadas, através da tríade rede-individualização-aprendizagem, constituem normalidades diferenciais nos sujeitos com deficiência. This dissertation aims to understand how support practices to school inclusion have put into operation normalization processes of people with disabilities since the 1990s. In order to do that, 11 national and international policies regulating practices of school inclusion in Brazil from 1990 to 2015 were used as empirical material. The materials were analyzed using the normalization tool, according to Michel Foucault. The analyses of the documents have evidenced support practices produced and required by inclusion policies, which aim to create conditions for keeping students with disabilities in the regular school. They have also shown both the necessary creation of network services and the circulation of the subjects in these services. Every professional participating in the service network produces a diagnosis based on their technical skills, with information that conveyed to the school. At school, information causes the individualization of educational interventions with the aim of developing learnings. It was concluded that outsourced support practices operate with normalization processes that not only are aimed at correcting, but also fragment the subject with disabilities by pointing out learning capabilities. It is defended the thesis that the outsourced support practices, through the network-individualization-learning triad, constitute differential normalities in subjects with disabilities.

APA, Harvard, Vancouver, ISO, and other styles

33

Mazumder, Sudip K. "Nonlinear Analysis and Control of Standalone, Parallel DC-DC, and Parallel Multi-Phase PWM Converters." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/28690.

Full text

Abstract:

Applications of distributed-power systems are on the rise. They are already used in telecommunication power supplies, aircraft and shipboard power-distribution systems, motor drives, plasma applications, and they are being considered for numerous other applications. The successful operation of these multi-converter systems relies heavily on a stable design. Conventional analyses of power converters are based on averaged models, which ignore the fast-scale instability and analyze the stability on a reduced-order manifold. As such, validity of the averaged models varies with the switching frequency even for the same topological structure. The prevalent procedure for analyzing the stability of switching converters is based on linearized smooth averaged (small-signal) models. Yet there are systems (in active use) that yield a non-smooth averaged model. Even for systems for which smooth averaged models are realizable, small-signal analyses of the nominal solution/orbit do not provide anything about three important characteristics: region of attraction of the nominal solution, dependence of the converter dynamics on the initial conditions of the states, and the post-instability dynamics. As such, converters designed based on small-signal analyses may be conservative. In addition, linear controllers based on such analysis may not be robust and optimal. Clearly, there is a need to analyze the stability of power converters from a different perspective and design nonlinear controllers for such hybrid systems. In this Dissertation, using bifurcation analysis and Lyapunov's method, we analyze the stability and dynamics of some of the building blocks of distributed-power systems, namely standalone, integrated, and parallel converters. Using analytical and experimental results, we show some of the differences between the conventional and new approaches for stability analyses of switching converters and demonstrate the shortcomings of some of the existing results. Furthermore, using nonlinear analyses we attempt to answer three fundamental questions: when does an instability occur, what is the mechanism of the instability, and what happens after the instability? Subsequently, we develop nonlinear controllers to stabilize parallel dc-dc and parallel multi-phase converters. The proposed controllers for parallel dc-dc converters combine the concepts of multiple-sliding-surface and integral-variable-structure control. They are easy to design, robust, and have good transient and steady-state performances. Furthermore, they achieve a constant switching frequency within the boundary layer and hence can be operated in interleaving or synchronicity modes. The controllers developed for parallel multi-phase converters retain many of the above features. In addition, they do not require any communication between the modules; as such, they have high redundancy. One of these control schemes combines space-vector modulation and variable-structure control. It achieves constant switching frequency within the boundary layer and a good compromise between the transient and steady-state performances. Ph. D.

APA, Harvard, Vancouver, ISO, and other styles

34

Nenad, Grahovac. "Анализа дисипације енергије у проблемима судара два или више тела". Phd thesis, Univerzitet u Novom Sadu, Fakultet tehničkih nauka u Novom Sadu, 2011. http://dx.doi.org/10.2298/NS20111208GRAHOVAC.

Full text

Abstract:

Анализиран је судар два тела као и дисипација енергије укључена кроз механизам сувог трења моделираног неглатком вишевредносном функцијом и кроз деформацију вискоеластичног штапа чији модел укључује фракционе изводе. Проблем судара два тела је приказан у форми Кошијевог проблема који припада класи неглатких вишевредносних диференцијалних једначина произвољног реалногреда. Кошијев проблем је решен нумеричким поступком заснованим на Тарнеровом алгоритму. Испитано је кретање система и дисипација енергије за разне вредности улазних параметара. Показано је да се уведене методе могу применити и на проблем судара три тела. Analiziran je sudar dva tela kao i disipacija energije uključena kroz mehanizam suvog trenja modeliranog neglatkom viševrednosnom funkcijom i kroz deformaciju viskoelastičnog štapa čiji model uključuje frakcione izvode. Problem sudara dva tela je prikazan u formi Košijevog problema koji pripada klasi neglatkih viševrednosnih diferencijalnih jednačina proizvoljnog realnogreda. Košijev problem je rešen numeričkim postupkom zasnovanim na Tarnerovom algoritmu. Ispitano je kretanje sistema i disipacija energije za razne vrednosti ulaznih parametara. Pokazano je da se uvedene metode mogu primeniti i na problem sudara tri tela. Impact of two bodies was analyzed as well as energy dissipation, which was included through dry friction phenomena modelled by a set-valued function, and through deformation of a viscoelastic rod modelled by fractional derivatives. The impact problem was presented in the form of the Cauchy problem that belongs to a class of set-valued fractional differential equations. The Cauchy problem was solved by the numerical procedure based on Turner’s algorithm. Behaviour and energy dissipation of the system was investigated for different values of input parameters. It was shown that suggested procedure can be applied on the problem of impact of three bodies.

APA, Harvard, Vancouver, ISO, and other styles

35

Kurz, Joshua J. "The Figure of the Refugee." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1397230693.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Kuiava, Roman. "Projeto de controladores para o amortecimento de oscilações em sistemas elétricos com geração distribuída." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/18/18154/tde-25032010-093826/.

Full text

Abstract:

Essa pesquisa se propõe a investigar o uso de Inclusões Diferenciais Lineares Limitadas por Norma (IDLNs) para projeto de controladores de amortecimento de tipo PSS (Power System Stabilizer) para sistemas elétricos com a presença de geração distribuída. Uma vez definida de maneira adequada, uma IDLN pode ser capaz de englobar um conjunto de trajetórias do modelo não-linear do sistema em estudo. Assim, é possível garantir certas propriedades (estabilidade assintótica, por exemplo) para as trajetórias da IDLN e, consequentemente, as mesmas propriedades terão validade para as trajetórias do modelo não-linear. Inicialmente propõe-se um procedimento para cálculo dos parâmetros do modelo de IDLN proposto de forma que ela seja capaz de agregar um conjunto de dinâmicas de interesse do sistema. Tal procedimento divide-se, basicamente, em duas etapas. Na primeira etapa, o objetivo é englobar um conjunto de trajetórias do modelo não-linear do sistema numa Inclusão Diferencial Linear Politópica (IDLP). Já na segunda etapa, os parâmetros da IDLN são calculados a partir da solução um problema na forma de LMIs (Linear Matrix Inequalities) que utiliza informações da IDLP obtida anteriormente. Em seguida, essa pesquisa propõe um procedimento sistemático na forma de LMIs para projeto de controladores de amortecimento de tipo PSS para sistemas de geração distribuída usando-se os modelos de IDLNs propostos. Restrições na forma de desigualdades matriciais são incluídas ao problema de controle para garantir um desempenho mínimo a ser atingido pelo controlador. Como resultado, a formulação do problema de controle é descrita por um conjunto de BMIs (Bilinear Matrix Inequalities). Entretanto, através de um procedimento de separação pode-se tratar o problema em duas etapas, ambas envolvendo a solução de um conjunto de LMIs. Uma planta de co-geração instalada numa rede de distribuição composta por um alimentador e 6 barras é utilizada como sistema teste. This work proposes an investigation about the use of Norm-bounded Linear Differential Inclusions (NLDIs) for the design of PSS-type damping controllers for electrical systems with the presence of distributed generation. When the NLDI is properly defined, it is possible to guarantee certain properties (for example, asymptotic stability) to the trajectories of the NLDI and, consequently, the trajectories of the nonlinear model have these same properties. Initially, this research proposes a procedure to calculate the NLDI parameters in such way it can be capable to aggregate a set of dynamics of interest. Such procedure is constituted by two steps. In the first step, the objective is to aggregate some trajectories of the nonlinear model to a Politopic Linear Differential Inclusion (PLDI). In the second step, the NLDI parameters are calculated by solving a problem in the form of LMIs (Linear Matrix Inequalities) that uses the IDLP previously obtained. After that, this research proposes a systematic method based on LMIs for the design of PSS-type damping controllers for distributed generation systems. Such method uses the proposed NLDI models. Constraints in the form of LMIs are included to the control problem formulation in order to guarantee a desirable performance to the controller. As a result, the control problem formulation is structured by a set of BMIs (Bilinear Matrix Inequalities). However, it is possible to deal with such problem in two steps,both involving the solution of a set of LMIs. A cogeneration plant added to a distribution network constituted by a feeder and six buses is adopted as test system.

APA, Harvard, Vancouver, ISO, and other styles

37

Torres, Mónica. "Plane-like minimal surfaces in periodic media with inclusions." Thesis, 2002. http://hdl.handle.net/2152/999.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Torres, Monica. "Plane-like minimal surfaces in periodic media with inclusions." 2002. http://wwwlib.umi.com/cr/utexas/fullcit?p3086718.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Fischer, Julia [Verfasser]. "Optimal control problems governed by nonlinear partial differential equations and inclusions / vorgelegt von Julia Fischer." 2010. http://d-nb.info/1004057067/34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Gotika, Priyanka. "Non-smooth Dynamics Using Differential-algebraic Equations Perspective: Modeling and Numerical Solutions." Thesis, 2011. http://hdl.handle.net/1969.1/ETD-TAMU-2011-12-10226.

Full text

Abstract:

This thesis addressed non-smooth dynamics of lumped parameter systems, and was restricted to Filippov-type systems. The main objective of this thesis was twofold. Firstly, modeling aspects of Filippov-type non-smooth dynamical systems were addressed with an emphasis on the constitutive assumptions and mathematical structure behind these models. Secondly, robust algorithms were presented to obtain numerical solutions for various Filippov-type lumped parameter systems. Governing equations were written using two different mathematical approaches. The first approach was based on differential inclusions and the second approach was based on differential-algebraic equations. The differential inclusions approach is more amenable to mathematical analysis using existing mathematical tools. On the other hand, the approach based on differential-algebraic equations gives more insight into the constitutive assumptions of a chosen model and easier to obtain numerical solutions. Bingham-type models in which the force cannot be expressed in terms of kinematic variables but the kinematic variables can be expressed in terms of force were considered. Further, Coulomb friction was considered in which neither the force can be expressed in terms of kinematic variables nor the kinematic variables in terms of force. However, one can write implicit constitutive equations in terms of kinematic quantities and force. A numerical framework was set up to study such systems and the algorithm was devised. Towards the end, representative dynamical systems of practical significance were considered. The devised algorithm was implemented on these systems and the results were obtained. The results show that the setting offered by differential-algebraic equations is appropriate for studying dynamics of lumped parameter systems under implicit constitutive models.

APA, Harvard, Vancouver, ISO, and other styles

41

Matusik, Radosław. "Stabilność sieci neuronowej w skończonym czasie." Doctoral thesis, 2014. https://depotuw.ceon.pl/handle/item/2067.

Full text

Abstract:

W rozprawie zajmujemy się badaniem globalnej stabilności w skończonym czasie pewnych klas sieci neuronowych typu Hopfielda. Rozważane przez nas sieci mogą być opisane zarówno układem równań różniczkowych, jak też inkluzją różniczkową, których prawe strony spełniają warunki typu Caratheodory'ego. W celu wykazania globalnej stabilności w skończonym czasie wykorzystujemy zależną od czasu funkcję Lapunowa, która jest jedynie ciągła. W rozprawie udowadniamy twierdzenia o globalnej stabilności w skończonym czasie dla układu równań różniczkowych oraz inkluzji różniczkowej i w konsekwencji dla sieci neuronowych typu Hopfielda. Podajemy także wzór na tzw. funkcję czasu osadzania, która daje informację po jakim czasie sieć neuronowa będzie stabilna. W pracy konstruujemy przykłady (również numeryczne) konkretnych sieci neuronowych typu Hopfielda, które są globalnie stabilne w skończonym czasie. The aim of this dissertation is to study global finite-time stability of some classes of Hopfield neural network. Neural networks which are considered in this dissertation, are described by system of differential equations as well as differential inclusion, whose right-hand sides satisfy Caratheodory conditions. In order to prove global stability in finite time, time-dependent, but only continuous Lyapunov function is applied. In the dissertation there are proved global finite-time stability theorems for system of differential equations, differential inclusion and hence for Hopfield neural network. There is also given the formula for the settling-time function, which gives us information when neural network will be stable in finite time. In this dissertation there are constructed examples (also numerical) of Hopfield neural networks, which are globally stable in finite time.

APA, Harvard, Vancouver, ISO, and other styles

42

Akhil, P. T. "Topics in Network Utility Maximization : Interior Point and Finite-step Methods." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/3268.

Full text

Abstract:

Network utility maximization has emerged as a powerful tool in studying flow control, resource allocation and other cross-layer optimization problems. In this work, we study a flow control problem in the optimization framework. The objective is to maximize the sum utility of the users subject to the flow constraints of the network. The utility maximization is solved in a distributed setting; the network operator does not know the user utility functions and the users know neither the rate choices of other users nor the flow constraints of the network. We build upon a popular decomposition technique proposed by Kelly [Eur. Trans. Telecommun., 8(1), 1997] to solve the utility maximization problem in the aforementioned distributed setting. The technique decomposes the utility maximization problem into a user problem, solved by each user and a network problem solved by the network. We propose an iterative algorithm based on this decomposition technique. In each iteration, the users communicate to the network their willingness to pay for the network resources. The network allocates rates in a proportionally fair manner based on the prices communicated by the users. The new feature of the proposed algorithm is that the rates allocated by the network remains feasible at all times. We show that the iterates put out by the algorithm asymptotically tracks a differential inclusion. We also show that the solution to the differential inclusion converges to the system optimal point via Lyapunov theory. We use a popular benchmark algorithm due to Kelly et al. [J. of the Oper. Res. Soc., 49(3), 1998] that involves fast user updates coupled with slow network updates in the form of additive increase and multiplicative decrease of the user flows. The proposed algorithm may be viewed as one with fast user update and fast network update that keeps the iterates feasible at all times. Simulations suggest that our proposed algorithm converges faster than the aforementioned benchmark algorithm. When the flows originate or terminate at a single node, the network problem is the maximization of a so-called d-separable objective function over the bases of a polymatroid. The solution is the lexicographically optimal base of the polymatroid. We map the problem of finding the lexicographically optimal base of a polymatroid to the geometrical problem of finding the concave cover of a set of points on a two-dimensional plane. We also describe an algorithm that finds the concave cover in linear time. Next, we consider the minimization of a more general objective function, i.e., a separable convex function, over the bases of a polymatroid with a special structure. We propose a novel decomposition algorithm and show the proof of correctness and optimality of the algorithm via the theory of polymatroids. Further, motivated by the need to handle piece-wise linear concave utility functions, we extend the decomposition algorithm to handle the case when the separable convex functions are not continuously differentiable or not strictly convex. We then provide a proof of its correctness and optimality.

APA, Harvard, Vancouver, ISO, and other styles

43

Akhil, P. T. "Topics in Network Utility Maximization : Interior Point and Finite-step Methods." Thesis, 2017. http://hdl.handle.net/2005/3268.

Full text

Abstract:

Network utility maximization has emerged as a powerful tool in studying flow control, resource allocation and other cross-layer optimization problems. In this work, we study a flow control problem in the optimization framework. The objective is to maximize the sum utility of the users subject to the flow constraints of the network. The utility maximization is solved in a distributed setting; the network operator does not know the user utility functions and the users know neither the rate choices of other users nor the flow constraints of the network. We build upon a popular decomposition technique proposed by Kelly [Eur. Trans. Telecommun., 8(1), 1997] to solve the utility maximization problem in the aforementioned distributed setting. The technique decomposes the utility maximization problem into a user problem, solved by each user and a network problem solved by the network. We propose an iterative algorithm based on this decomposition technique. In each iteration, the users communicate to the network their willingness to pay for the network resources. The network allocates rates in a proportionally fair manner based on the prices communicated by the users. The new feature of the proposed algorithm is that the rates allocated by the network remains feasible at all times. We show that the iterates put out by the algorithm asymptotically tracks a differential inclusion. We also show that the solution to the differential inclusion converges to the system optimal point via Lyapunov theory. We use a popular benchmark algorithm due to Kelly et al. [J. of the Oper. Res. Soc., 49(3), 1998] that involves fast user updates coupled with slow network updates in the form of additive increase and multiplicative decrease of the user flows. The proposed algorithm may be viewed as one with fast user update and fast network update that keeps the iterates feasible at all times. Simulations suggest that our proposed algorithm converges faster than the aforementioned benchmark algorithm. When the flows originate or terminate at a single node, the network problem is the maximization of a so-called d-separable objective function over the bases of a polymatroid. The solution is the lexicographically optimal base of the polymatroid. We map the problem of finding the lexicographically optimal base of a polymatroid to the geometrical problem of finding the concave cover of a set of points on a two-dimensional plane. We also describe an algorithm that finds the concave cover in linear time. Next, we consider the minimization of a more general objective function, i.e., a separable convex function, over the bases of a polymatroid with a special structure. We propose a novel decomposition algorithm and show the proof of correctness and optimality of the algorithm via the theory of polymatroids. Further, motivated by the need to handle piece-wise linear concave utility functions, we extend the decomposition algorithm to handle the case when the separable convex functions are not continuously differentiable or not strictly convex. We then provide a proof of its correctness and optimality.

APA, Harvard, Vancouver, ISO, and other styles

44

Cheng, Jinn-Shing, and 鄭進興. "Research on Robust Stability of Multivariable Feedback Control Systems : Differential Inclusion Approach." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/47352457064514617800.

Full text

Abstract:

博士 國立中山大學 電機工程研究所 83 In this thesis, we explore the state feedback control of nonlinear uncertain dynamical systems. For many practical applications, there is need to consider more general types of uncertainties or there is need to use some discontinuous control. These make the traditional theory of ordinary differential equations unapplicable for both analysis and synthesis purposes, i.e., the traditional Carathodory concepts become useless. Consequently, we will use more general differential inclusions to describe the dynamics of the nonlinear uncertain systems. Adopting the problem formulation based on differential inclusions, we determine a linear state feedback control via a suitable choice of control parameters for solving an algebraic Riccati equation that guarantees all trajectories of differential-included uncertain dynamical systems exhibit "stable" behavior. We also consider the robust tracking control problem of nonlinear differential-included uncertain systems. The goal is to find a generalized feedback control such that the pre-specified single-valued continuously differentiable observation map is a solution to the first-order partial differential inclusions. In other words, some solutions of these nonlinear differential-included uncertain systems are linked by this observation map, in the sense that its graph is a viable manifold. Furthermore, we shall study the problem of regulating control systems in the framework of viability theory. This amounts to saying that the solutions of the nonlinear differential-included uncertain systems must obey constraints, called viability constraints. Therefore,the goal is to introduce the feedback control such that the trajectories are viable in a given set.

APA, Harvard, Vancouver, ISO, and other styles

45

土井, 英樹, and Hideki Doi. "p62/SQSTM1 Differentially Removes the Toxic Mutant Androgen Receptor via Autophagy and Inclusion Formation in a Spinal and Bulbar Muscular Atrophy Mouse Model." Thesis, 2013. http://hdl.handle.net/2237/19018.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Dinevari, Toktam. "Fixed point results for multivalued contractions on graphs and their applications." Thèse, 2015. http://hdl.handle.net/1866/12344.

Full text

Abstract:

Nous présentons dans cette thèse des théorèmes de point fixe pour des contractions multivoques définies sur des espaces métriques, et, sur des espaces de jauges munis d’un graphe. Nous illustrons également les applications de ces résultats à des inclusions intégrales et à la théorie des fractales. Cette thèse est composée de quatre articles qui sont présentés dans quatre chapitres. Dans le chapitre 1, nous établissons des résultats de point fixe pour des fonctions multivoques, appelées G-contractions faibles. Celles-ci envoient des points connexes dans des points connexes et contractent la longueur des chemins. Les ensembles de points fixes sont étudiés. La propriété d’invariance homotopique d’existence d’un point fixe est également établie pour une famille de Gcontractions multivoques faibles. Dans le chapitre 2, nous établissons l’existence de solutions pour des systèmes d’inclusions intégrales de Hammerstein sous des conditions de type de monotonie mixte. L’existence de solutions pour des systèmes d’inclusions différentielles avec conditions initiales ou conditions aux limites périodiques est également obtenue. Nos résultats s’appuient sur nos théorèmes de point fixe pour des G-contractions multivoques faibles établis au chapitre 1. Dans le chapitre 3, nous appliquons ces mêmes résultats de point fixe aux systèmes de fonctions itérées assujettis à un graphe orienté. Plus précisément, nous construisons un espace métrique muni d’un graphe G et une G-contraction appropriés. En utilisant les points fixes de cette G-contraction, nous obtenons plus d’information sur les attracteurs de ces systèmes de fonctions itérées. Dans le chapitre 4, nous considérons des contractions multivoques définies sur un espace de jauges muni d’un graphe. Nous prouvons un résultat de point fixe pour des fonctions multivoques qui envoient des points connexes dans des points connexes et qui satisfont une condition de contraction généralisée. Ensuite, nous étudions des systèmes infinis de fonctions itérées assujettis à un graphe orienté (H-IIFS). Nous donnons des conditions assurant l’existence d’un attracteur unique à un H-IIFS. Enfin, nous appliquons notre résultat de point fixe pour des contractions multivoques définies sur un espace de jauges muni d’un graphe pour obtenir plus d’information sur l’attracteur d’un H-IIFS. Plus précisément, nous construisons un espace de jauges muni d’un graphe G et une G-contraction appropriés tels que ses points fixes sont des sous-attracteurs du H-IIFS. In this thesis, we present fixed point theorems for multivalued contractions defined on metric spaces, and, on gauge spaces endowed with directed graphs. We also illustrate the applications of these results to integral inclusions and to the theory of fractals. chapters. In Chapter 1, we establish fixed point results for the maps, called multivalued weak G-contractions, which send connected points to connected points and contract the length of paths. The fixed point sets are studied. The homotopical invariance property of having a fixed point is also established for a family of weak G-contractions. In Chapter 2, we establish the existence of solutions of systems of Hammerstein integral inclusions under mixed monotonicity type conditions. Existence of solutions to systems of differential inclusions with initial value condition or periodic boundary value condition are also obtained. Our results rely on our fixed point theorems for multivalued weak G-contractions established in Chapter 1. In Chapter 3, those fixed point results for multivalued G-contractions are applied to graph-directed iterated function systems. More precisely, we construct a suitable metric space endowed with a graph G and an appropriate G-contraction. Using the fixed points of this G-contraction, we obtain more information on the attractors of graph-directed iterated function systems. In Chapter 4, we consider multivalued maps defined on a complete gauge space endowed with a directed graph. We establish a fixed point result for maps which send connected points into connected points and satisfy a generalized contraction condition. Then, we study infinite graph-directed iterated function systems (H-IIFS). We give conditions insuring the existence of a unique attractor to an H-IIFS. Finally, we apply our fixed point result for multivalued contractions on gauge spaces endowed with a graph to obtain more information on the attractor of an H-IIFS. More precisely, we construct a suitable gauge space endowed with a graph G and a suitable multivalued G-contraction such that its fixed points are sub-attractors of the H-IIFS.

APA, Harvard, Vancouver, ISO, and other styles

47

Ferreira, Angélica. "COMO CONSTRÕEM AS EDUCADORAS A SUA PRÁTICA PEDAGÓGICA COM CRIANÇAS COM TRANSTORNO DO ESPETRO DO AUTISMO?" Master's thesis, 2018. http://hdl.handle.net/10400.26/35706.

Full text

Abstract:

A problemática do Transtorno do Espetro do Autismo (TEA) tem sido alvo de muita investigação ao longo dos anos. O DSM V – Manual Diagnóstico e Estatístico de Transtornos Mentais, em 2013, provocou modificações significativas no paradigma do autismo e respetivos Transtornos do Neurodesenvolvimento. A publicação do DSM-V é uma atualização da investigação/estudo sobre as várias perturbações, nomeadamente sobre o autismo, e teve, inclusivamente, como consequência a alteração da designação. O interesse pela temática deste trabalho de pesquisa surgiu no decorrer de um estágio curricular, numa sala de Jardim de Infância, que tinha no seio do seu grupo uma criança com TEA. Partindo deste interesse, estabeleceram-se como objetivos deste trabalho, compreender e conhecer as Práticas Pedagógicas Inclusivas das Educadoras de Infância com crianças com TEA. Este trabalho tem como objetivo entender o trabalho das educadoras de infância e a sua Prática Pedagógica com crianças com Transtorno de Espetro do Autismo. Para isso foi feito uma revisão da literatura e foram realizadas Entrevistas a educadoras de Infância no distrito de Santarém. The problem of Autism Spectrum Disorder (ASD) has been the subject of much research over the years. The DSM V - Diagnostic and Statistical Manual of Mental Disorders, in 2013, caused significant changes in the paradigm of autism and its neurodevelopmental disorders. The publication of the DSM-V is an update of the research / study on the various disorders, namely on autism, and has, as a consequence, changed the designation. The interest in the theme of this research work arose during a curricular internship in a Kindergarten room, which had a child with ASD in its group. Based on this interest, the aims of this work were to know and understand the Inclusive Pedagogical Practices of Childhood Educators with children with ASD. This work aims to understand the work of the educators of childhood and its Pedagogical Practice with children with Autism Spectrum Disorder. For this, a review of the literature was made and interviews were conducted with childhood educators in the district of Santarém.

APA, Harvard, Vancouver, ISO, and other styles

48

Simon, Thilo Martin. "Materials Science-inspired problems in the Calculus of Variations: Rigidity of shape memory alloys and multi-phase mean curvature flow." 2017. https://ul.qucosa.de/id/qucosa%3A31846.

Full text

Abstract:

This thesis is concerned with two problems in the Calculus of Variations touching on two central aspects of Materials Science: the structure of solid matter and its dynamic behavior. The problem pertaining to the first aspect is the analysis of the rigidity properties of possibly branched microstructures formed by shape memory alloys undergoing cubic-to-tetragonal transformations. On the basis of a variational model in the framework of linearized elasticity, we derive a non-convex and non-discrete valued differential inclusion describing the local volume fractions of such structures. Our main result shows the inclusion to be rigid without additional regularity assumptions and provides a list of all possible solutions. We give constructions ensuring that the various types of solutions indeed arise from the variational model and quantitatively describe their rigidity via H-measures. Our contribution to the second aspect is a conditional result on the convergence of the Allen-Cahn Equations to multi-phase mean curvature flow, which is a popular model for grain growth in polychrystalline metals. The proof relies on the gradient flow structure of both models and borrows ideas from certain convergence proofs for minimizing movement schemes.:1 Introduction 1.1 Shape memory alloys 1.2 Multi-phase mean curvature flow 2 Branching microstructures in shape memory alloys: Rigidity due to macroscopic compatibility 2.1 The main rigidity theorem 2.2 Outline of the proof 2.3 Proofs 3 Branching microstructures in shape memory alloys: Constructions 3.1 Outline and setup 3.2 Branching in two linearly independent directions 3.3 Combining all mechanisms for varying the volume fractions 4 Branching microstructures in shape memory alloys: Quantitative aspects via H-measures 4.1 Preliminary considerations 4.2 Structure of the H-measures 4.3 The transport property and accuracy of the approximation 4.4 Applications of the transport property 5 Convergence of the Allen-Cahn Equation to multi-phase mean curvature flow 5.1 Main results 5.2 Compactness 5.3 Convergence 5.4 Forces and volume constraints

APA, Harvard, Vancouver, ISO, and other styles

49

CUCINOTTA, SALVATORE. "Innovazioni tecnologiche in mangimistica per la valorizzazione delle biomasse residuali nel settore del petfood. Analisi delle caratteristiche macrostrutturali indotte dai processi di estrusione nella produzione di diete per cani con differenti livelli di inclusione di Pastazzo d’Arancia." Doctoral thesis, 2019. http://hdl.handle.net/11570/3146651.

Full text

Abstract:

Aim of the study was to evaluate the effect of inclusions of orange pulp (OP) at different dosages and of two different die diameter (Dd) during the extrusion of dog foods, on processing parameters, starch gelatinization (SG), in vitro digestibility of organic matter and kibble macrostructure. The experiment followed a 5x2 factorial arrangements, with 5 diets (4 experimental and 1 control) and 2 Dd, with a total of 10 diets. Five normal maintenance diets were formulated: four diets with different inclusions of OP (5%, 10%, 15% and 20%) in substitution of the corn meal and one diet without OP. The diet was manufactured in a single screw extruder with two die diameters (Dd) (5 and 7 mm), resulting in two die open areas of 19.6 mm2 and 39,5 mm2. The other extruder parameters were unchanged. Data were analyzed via ANOVA (SAS), considering the variables OP inclusion and Dd and their in-teractions and compared by polynomial contrasts (P<0.05). The increase of the OP concentration in the diets determined, during the extrusion, a reduction in radial expansion and piece volume and an increase in the longitudinal expansion and piece density. The best longitudinal expansion, obtained with OP, was associated with fiber structures consisting in a higher number of small cells with shapes closer to spheres. The changes in the parameters driving expansion could be due to the differences in the rheological properties between the continuous starch matrix and the OP particles, their interac-tion and their low physicochemical compatibility. Die diameter of 7 mm determined a reduction in radial expansion and piece volume and an increase in cutting force and in piece density. The specific mechanical energy - SME was significantly reduced by the increased Dd and OP inclusion. The die with diameter of 5 mm should be used for greater radial expansion and starch gelatinization. Further studies on the OP inclusion may clarify the influence of different fibers on palatability, sensory properties and acceptance by dogs. In the same way, it would be advantageous to regulate the water absorption/retention properties of these fibers, for their use as filling components in diets characterized by low energy content.

APA, Harvard, Vancouver, ISO, and other styles

Dissertations / Theses on the topic 'Differential inclusions'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles