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1
Andersson, Daniel. "Contributions to the Stochastic Maximum Principle." Doctoral thesis, KTH, Matematik (Avd.), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11301.
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This thesis consists of four papers treating the maximum principle for stochastic control problems. In the first paper we study the optimal control of a class of stochastic differential equations (SDEs) of mean-field type, where the coefficients are allowed to depend on the law of the process. Moreover, the cost functional of the control problem may also depend on the law of the process. Necessary and sufficient conditions for optimality are derived in the form of a maximum principle, which is also applied to solve the mean-variance portfolio problem. In the second paper, we study the problem of controlling a linear SDE where the coefficients are random and not necessarily bounded. We consider relaxed control processes, i.e. the control is defined as a process taking values in the space of probability measures on the control set. The main motivation is a bond portfolio optimization problem. The relaxed control processes are then interpreted as the portfolio weights corresponding to different maturity times of the bonds. We establish existence of an optimal control and necessary conditons for optimality in the form of a maximum principle, extended to include the family of relaxed controls. The third paper generalizes the second one by adding a singular control process to the SDE. That is, the control is singular with respect to the Lebesgue measure and its influence on the state is thus not continuous in time. In terms of the portfolio problem, this allows us to consider two investment possibilities - bonds (with a continuum of maturities) and stocks - and incur transaction costs between the two accounts. In the fourth paper we consider a general singular control problem. The absolutely continuous part of the control is relaxed in the classical way, i.e. the generator of the corresponding martingale problem is integrated with respect to a probability measure, guaranteeing the existence of an optimal control. This is shown to correspond to an SDE driven by a continuous orthogonal martingale measure. A maximum principle which describes necessary conditions for optimal relaxed singular control is derived.QC 20100618
2
Degla, Guy Aymard. "A Maximum Principle for Conjugate BVPs." Doctoral thesis, SISSA, 2001. http://hdl.handle.net/20.500.11767/4320.
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Fontana, Eleonora. "Maximum Principle for Elliptic and Parabolic Equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12061/.
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Nel primo capitolo si riporta il principio del massimo per operatori ellittici. Sarà considerato, in un primo momento, l'operatore di Laplace e, successivamente, gli operatori ellittici del secondo ordine, per i quali si dimostrerà anche il principio del massimo di Hopf. Nel secondo capitolo si affronta il principio del massimo per operatori parabolici e lo si utilizza per dimostrare l'unicità delle soluzioni di problemi ai valori al contorno.
4
Lobo, Pereira Fernando Manuel Ferreira. "A maximum principle for impulsive control systems." Thesis, Imperial College London, 1986. http://hdl.handle.net/10044/1/38084.
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Касьянов, Володимир, and Андрій Гончаренко. "SUBJECTIVE ENTROPY MAXIMUM PRINCIPLE AND ITS APPLICATIONS." Thesis, Національний авіаційний університет, 2017. https://er.nau.edu.ua/handle/NAU/48996.
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Касьянов, Володимир, and Андрій Гончаренко. "SUBJECTIVE ENTROPY MAXIMUM PRINCIPLE AND ITS APPLICATIONS." Thesis, Національний авіаційний університет, 2017. http://er.nau.edu.ua/handle/NAU/30676.
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Cai, Tingting. "The maximum power principle an empirical investigation /." [Gainesville, Fla.] : University of Florida, 2002. http://purl.fcla.edu/fcla/etd/UFE1000112.
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Thesis (Ph. D.)--University of Florida, 2002.Title from title page of source document. Document formatted into pages; contains vii, 175 p.; also contains graphics. Includes vita. Includes bibliographical references.
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Klinedinst, James. "A Maximum Principle in the Engel Group." Scholar Commons, 2014. https://scholarcommons.usf.edu/etd/5248.
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In this thesis, we will examine the properties of subelliptic jets in the Engel group of step 3. Step-2 groups, such as the Heisenberg group, do not provide insight into the general abstract calculations. This thesis then, is the first explicit non-trivial computation of the abstract results.
9
Whiting, Peter Mark. "Reflection traveltime tomography and the maximum entropy principle." Thesis, The University of Sydney, 1993. https://hdl.handle.net/2123/26623.
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Conventional reflection tomography creates an estimate of subsurface seismic velocity structure by inverting a set of seismic traveltime data. This is achieved by solving a least-squares optimisation problem that finds the velocity and depth model that minimises the difference between raytraced and measured traveltimes. Obtaining the traveltime data can be difficult as manual picking of reflection times is required and all picked reflection events must be associated with the reflector depths defined in the model. Even with good traveltime data the optimisation problem is very non-linear and the surface restriction of the sources and receivers makes the problem generally underdetermined. These issues result in severe ambiguity and local minima problems.
This thesis shows that modifications to the conventional reflection tomography algorithm can make it a more practical and reliable procedure that is less likely to be trapped by local minima. The ray tracing procedure is changed so that reflector depths are not necessary and automatic traveltime interpretation can be successful. Entropy constraints are introduced (after being justified) which prevent unwarranted velocity structure from appearing. This feature adds significant stability and reduces the ambiguity problems. Staged smoothing of the optimisation function helps avoid local minima.
Synthetic data examples show that the algorithm can be very effective on noise free data. Adding noise to synthetic data reduces the algorithms effectiveness, but inversions of real data sets produces updated velocity fields that result in superior pre-stack depth migrations.
10
Daghighi, Abtin. "The Maximum Principle for Cauchy-Riemann Functions and Hypocomplexity." Licentiate thesis, Mittuniversitetet, Institutionen för tillämpad naturvetenskap och design, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-17701.
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This licentiate thesis contains results on the maximum principle forCauchy–Riemann functions (CR functions) on weakly 1-concave CRmanifolds and hypocomplexity of locally integrable structures. Themaximum principle does not hold true in general for smooth CR functions,and basic counterexamples can be constructed in the presenceof strictly pseudoconvex points. We prove a maximum principle forcontinuous CR functions on smooth weakly 1-concave CR submanifolds.Because weak 1-concavity is also necessary for the maximumprinciple, a consequence is that a smooth generic CR submanifold ofCn obeys the maximum principle for continuous CR functions if andonly if it is weakly 1-concave. The proof is then generalized to embeddedweakly p-concave CR submanifolds of p-complete complexmanifolds. The second part concerns hypocomplexity and hypoanalyticstructures. We give a generalization of a known result regardingautomatic smoothness of solutions to the homogeneous problemfor the tangential CR vector fields given local holomorphic extension.This generalization ensures that a given locally integrable structureis hypocomplex at the origin if and only if it does not allow solutionsnear the origin which cannot be represented by a smooth function nearthe origin.Uppsatsen innehåller resultat om maximumprincipen för kontinuerligaCauchy–Riemann funktioner (CR-funktioner) på svagt 1-konkava CRmångfalder,samt hypokomplexitet för lokalt integrerbara strukturer.Maximumprincipen gäller inte generellt för släta CR funktioner ochmotexempel kan konstrueras givet strängt pseudokonvexa punkter.Vi bevisar en maximumprincip för kontinuerliga CR-funktioner påsläta inbäddade svagt 1-konkava CR-mångfalder. Eftersom svagt 1-konkavitet också är nödvändigt får vi som konsekvens att för slätageneriska inbäddade CR-mångfalder i Cn gäller att maximum-principenför kontinuerliga CR-funktioner håller om och endast om CR-mångfaldenär svagt 1-konkav. Vi generaliserar satsen till svagt p-konkava CRmångfalderi p-kompletta mångfalder. Den andra delen behandlarhypokomplexitet och hypoanalytiska strukturer. Vi generaliserar enkänd sats om automatisk släthet för lösningar till de tangentiella CRekvationerna,givet existensen av lokal holomorf utvidgning. Generaliseringenger att en lokalt integrerbar struktur är hypokomplex iorigo om och endast om den inte tillåter lösningar nära origo som inteär släta nära origo.
Forskning finansierad av Forskarskolan i Matematik och Beräkningsvetenskap (FMB), baserad i Uppsala.
11
Guo, Weiyu. "Implementing the principle of maximum entropy in option pricing /." free to MU campus, to others for purchase, 1999. http://wwwlib.umi.com/cr/mo/fullcit?p9946259.
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Felixová, Lucie. "Matematické metody teorie optimálního řízení a jejich užití." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2011. http://www.nusl.cz/ntk/nusl-229886.
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Tato diplomová práce se zabývá problematikou spojitého optimálního řízení, což je jedna z nejvýznamnějších aplikací teorie diferenciálních rovnic. Cílem této práce bylo jak nastudování matematické teorie optimálního řízení, tak především ukázat užití Pontrjaginova principu maxima a Bellmanova principu optimality při řešení vybraných úloh optimálního řízení. Důraz byl kladen především na problematiku časově a energeticky optimálního řízení elektrického vlaku, při zahrnutí kvadratické odporové funkce.
13
Le, Ngan Trang. "The positive maximum principle on Lie groups and symmetric spaces." Thesis, University of Sheffield, 2019. http://etheses.whiterose.ac.uk/22779/.
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In this thesis we will use harmonic analysis to get new results in probability on Lie groups and symmetric spaces. We will establish necessary and sufficient conditions for the existence of a square integrable K-bi-invariant density of a K-bi-invariant measure. We will show that there is a topological isomorphism between K-bi-invariant smooth functions and a subspace of the Sugiura space of rapidly decreasing functions. Furthermore, we will extend Courrège's classical results to Lie groups and symmetric spaces, this consists of characterizing all linear operators on the space of smooth functions with compact support, that satisfy the positive maximum principle, as Lévy- type operators. We will specify some conditions under which such operators map to the Banach space of continuous functions vanishing at infinity, this allows us to study Feller semigroups and their generator in this context. We will show that on compact Lie groups all linear operators satisfying the positive maximum principle can be represented as pseudo-differential operators and on compact symmetric spaces they have analogous representations called spherical pseudo-differential operators.
14
Santos, Telma João da Fonseca. "Some versions of the maximum principle for elliptic integral functionals." Doctoral thesis, Universidade de Évora, 2011. http://hdl.handle.net/10174/17940.
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O Princípio do Máximo Forte (PMF) é uma propriedade bem conhecida que pode ser vista como um resultado de unicidade para soluções de Equações Diferenciais Parciais. Através das condições necessárias de optimalidade, à também aplicável a algumas classes de problemas variacionais. O trabalho é dedicado a várias versões do PMF em tal contexto variacional, que sê verificam mesmo quando as respectivas equações de Euler-Lagrange não são válidas. Provarmos PMF variacionais para algum tipo de funcionais integrais no sentido tradicional, e obtemos uma extensão deste princípio, que pode ser visto como r:ma propriedade extremal de uma série de funções específicas. ABSTRACT: The Strong Maximum Principle (SMP) is a well-known property, which can be recognized as a kind of uniqueness result for solutions of Partial Differential Equations. Through the necessary conditions of optimality it is applicable to minimizers in some classes of variational problems as well. The work is devoted to various versions of SMP in such variational setting, which hold also if the respective Euler-Lagrange equations are no longer valid. We prove variational SMP for some types of integral functionals in the traditional sense as well a-s obtain an extension of this principle, which can be seen as an extremal property of a series of specific functions.
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Camiola, Vito Dario. "Subbands model for semiconductors based on the Maximum Entropy Principle." Doctoral thesis, Università di Catania, 2013. http://hdl.handle.net/10761/1313.
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In this thesis a double-gate MOSFET is simulated with an energy-transport subband model and an energy-transport model is derived for a nanoscale MOSFET.
Regarding the double-gate MOSFET the model is formulated starting from the moment system derived from the Schroedinger-Poisson-Boltzmann equations. The system is closed on the basis of the maximum entropy principle and includes scattering of electrons with acoustic and non-polar optical phonons. The proposed
expression of the entropy combines quantum effects and semiclassical transport by weighting the contribution of each sub band with the square modulus of the envelope functions arising from the Schroedinger-Poisson system. The simulations show that the model is able to capture the relevant confining and transport features and asses the robustness of the numerical scheme.\\
The model for the MOSFET takes into account the presence of both 3D and 2D electron gas included along with the quantization in the transversal direction with respect to the oxide at the gate which gives raise to a sub band decomposition of the electron energy.\\
Both intra and inter scattering between the 2D and the 3D electron gas are considered. In particular, a fictitious transition from the 3D to the 2D electrons and vice versa is introduced.
16
Ziebart, Brian D. "Modeling Purposeful Adaptive Behavior with the Principle of Maximum Causal Entropy." Research Showcase @ CMU, 2010. http://repository.cmu.edu/dissertations/17.
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Predicting human behavior from a small amount of training examples is a challenging machine learning problem. In this thesis, we introduce the principle of maximum causal entropy, a general technique for applying information theory to decision-theoretic, game-theoretic, and control settings where relevant information is sequentially revealed over time. This approach guarantees decision-theoretic performance by matching purposeful measures of behavior (Abbeel & Ng, 2004), and/or enforces game-theoretic rationality constraints (Aumann, 1974), while otherwise being as uncertain as possible, which minimizes worst-case predictive log-loss (Gr¨unwald & Dawid, 2003).
We derive probabilistic models for decision, control, and multi-player game settings using this approach. We then develop corresponding algorithms for efficient inference that include relaxations of the Bellman equation (Bellman, 1957), and simple learning algorithms based on convex optimization. We apply the models and algorithms to a number of behavior prediction tasks. Specifically, we present empirical evaluations of the approach in the domains of vehicle route preference modeling using over 100,000 miles of collected taxi driving data, pedestrian motion modeling from weeks of indoor movement data, and robust prediction of game play in stochastic multi-player games.
17
Santos, Telma João. "Some versions of the Strong Maximum Principal for elliptic integral functionals." Doctoral thesis, Universidade de Évora, 2011. http://hdl.handle.net/10174/9506.
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The Strong Maximum Principle (SMP) is a well-known property, which can be recognized as a kind of uniqueness result for solutions of Partial Differential Equations. Through the necessary conditions of optimality it is applicable to minimizers in some classes of variational problems as well. The work is devoted to various versions of SMP in such variational setting, which hold also if the respective Euler-Lagrange equations are no longer valid. We prove variational SMP for some types of integral functionals in the traditional sense as well as obtain an extension of this principle, which can be seen as an extremal property of a series of specific functions.
18
LeBlanc, Raymond. "The maximum entropy principle as a basis for statistical models in epidemiology /." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74600.
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We propose an approach for the construction of statistical models based on the maximum entropy principle in conjunction with a constructive method relying on a precise description of the individual contribution of each possible unit of observation of the population. This procedure is applied to the analysis of 2 x 2 tables, ubiquitous in biostatistics. This approach provides a new perspective and understanding of the fundamental nature of logistic regression, of Cox's proportional hazard model and of the noncentral hypergeometric model. Application of this method to analyse the odds ratio produces new distributions for this random variable and gives new means of estimating the odds ratio by confidence intervals. We present basic properties of these distributions and compare results with other methods.Finally, this constructive approach that proceeds from the lower level of the individual contribution of the experimental units to the global level of the population is applied to sample size determination for comparative studies when, in the compared groups, there is attrition due to noncompliance to the specific regimen. This attrition reduces the apparent treatment effect in the analysis. This presentation constitutes a foundation for a more general and elegant solution to the problem.
19
Fu, Guanxing. "Maximum Principle for Reflected BSPDE and Mean Field Game Theory with Applications." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19248.
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Diese Arbeit behandelt zwei Gebiete: stochastische partielle Rückwerts-Differentialgleichungen (BSPDEs) und Mean-Field-Games (MFGs).
Im ersten Teil wird über eine stochastische Variante der De Giorgischen Iteration ein Maximumprinzip für quasilineare reflektierte BSPDEs (RBSPDEs) auf allgemeinen Gebieten bewiesen. Als Folgerung erhalten wir ein Maximumprinzip für RBSPDEs auf beschränkten, sowie für BSPDEs auf allgemeinen Gebieten. Abschließend wird das lokale Verhalten schwacher Lösungen untersucht.
Im zweiten Teil zeigen wir zunächst die Existenz von Gleichgewichten in MFGs mit singulärer Kontrolle. Wir beweisen, dass die Lösung eines MFG ohne Endkosten und ohne Kosten in der singulären Kontrolle durch die Lösungen eines MFGs mit strikt regulären Kontrollen approximiert werden kann. Die vorgelegten Existenz- und Approximationsresultat basieren entscheidend auf der Wahl der Storokhod M1 Topologie auf dem Raum der Càdlàg-Funktion.
Anschließend betrachten wir ein MFG optimaler Portfolioliquidierung unter asymmetrischer Information. Die Lösung des MFG charakterisieren wir über eine stochastische Vorwärts-Rückwärts-Differentialgleichung (FBSDE) mit singulärer Endbedingung der Rückwärtsgleichung oder alternativ über eine FBSDE mit endlicher Endbedingung, jedoch singulärem Treiber. Wir geben ein Fixpunktargument, um die Existenz und Eindeutigkeit einer Kurzzeitlösung in einem gewichteten Funktionenraum zu zeigen. Dies ermöglicht es, das ursprüngliche MFG mit entsprechenden MFGs ohne Zustandsendbedinung zu approximieren.
Der zweite Teil wird abgeschlossen mit einem Leader-Follower-MFG mit Zustandsendbedingung im Kontext optimaler Portfolioliquidierung bei hierarchischer
Agentenstruktur. Wir zeigen, dass das Problem beider Spielertypen auf singuläre FBSDEs zurückgeführt werden kann, welche mit ähnlichen Methoden wie im vorangegangen Abschnitt behandelt werden können.The thesis is concerned with two topics: backward stochastic partial differential equations and mean filed games. In the first part, we establish a maximum principle for quasi-linear reflected backward stochastic partial differential equations (RBSPDEs) on a general domain by using a stochastic version of De Giorgi’s iteration. The maximum principle for RBSPDEs on a bounded domain and the maximum principle for BSPDEs on a general domain are obtained as byproducts. Finally, the local behavior of the weak solutions is considered. In the second part, we first establish the existence of equilibria to mean field games (MFGs) with singular controls. We also prove that the solutions to MFGs with no terminal cost and no cost from singular controls can be approximated by the solutions, respectively control rules, for MFGs with purely regular controls. Our existence and approximation results strongly hinge on the use of the Skorokhod M1 topology on the space of càdlàg functions. Subsequently, we consider an MFG of optimal portfolio liquidation under asymmetric information. We prove that the solution to the MFG can be characterized in terms of a forward backward stochastic differential equation (FBSDE) with possibly singular terminal condition on the backward component or, equivalently, in terms of an FBSDE with finite terminal value, yet singular driver. We apply the fixed point argument to prove the existence and uniqueness on a short time horizon in a weighted space. Our existence and uniqueness result allows to prove that our MFG can be approximated by a sequence of MFGs without state constraint. The final result of the second part is a leader follower MFG with terminal constraint arising from optimal portfolio liquidation between hierarchical agents. We show the problems for both follower and leader reduce to the solvability of singular FBSDEs, which can be solved by a modified approach of the previous result.
20
Tommasoli, Andrea <1976>. "Maximum principle, mean value operators and quasi boundedness in non-euclidean settings." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2008. http://amsdottorato.unibo.it/949/1/Tesi_Tommasoli_Andrea.pdf.
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This work deals with some classes of linear second order partial differential
operators with non-negative characteristic form and underlying non-
Euclidean structures. These structures are determined by families of locally
Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot-
Carath´eodory type. The Carnot-Carath´eodory metric related to a family
{Xj}j=1,...,m is the control distance obtained by minimizing the time needed
to go from two points along piecewise trajectories of vector fields. We are
mainly interested in the causes in which a Sobolev-type inequality holds with
respect to the X-gradient, and/or the X-control distance is Doubling with
respect to the Lebesgue measure in RN. This study is divided into three
parts (each corresponding to a chapter), and the subject of each one is a
class of operators that includes the class of the subsequent one.
In the first chapter, after recalling “X-ellipticity” and related concepts
introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle
for linear second order differential operators for which we only assume
a Sobolev-type inequality together with a lower terms summability. Adding
some crucial hypotheses on measure and on vector fields (Doubling property
and Poincar´e inequality), we will be able to obtain some Liouville-type results.
This chapter is based on the paper [GL03] by Guti´errez and Lanconelli.
In the second chapter we treat some ultraparabolic equations on Lie
groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results
of Cinti [Cin07] about this class of operators and associated potential theory,
we prove a scalar convexity for mean-value operators of L-subharmonic
functions, where L is our differential operator.
In the third chapter we prove a necessary and sufficient condition of regularity,
for boundary points, for Dirichlet problem on an open subset of RN related
to sub-Laplacian. On a Carnot group we give the essential background
for this type of operator, and introduce the notion of “quasi-boundedness”.
Then we show the strict relationship between this notion, the fundamental
solution of the given operator, and the regularity of the boundary points.
21
Tommasoli, Andrea <1976>. "Maximum principle, mean value operators and quasi boundedness in non-euclidean settings." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2008. http://amsdottorato.unibo.it/949/.
Full textAbstract:
This work deals with some classes of linear second order partial differential
operators with non-negative characteristic form and underlying non-
Euclidean structures. These structures are determined by families of locally
Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot-
Carath´eodory type. The Carnot-Carath´eodory metric related to a family
{Xj}j=1,...,m is the control distance obtained by minimizing the time needed
to go from two points along piecewise trajectories of vector fields. We are
mainly interested in the causes in which a Sobolev-type inequality holds with
respect to the X-gradient, and/or the X-control distance is Doubling with
respect to the Lebesgue measure in RN. This study is divided into three
parts (each corresponding to a chapter), and the subject of each one is a
class of operators that includes the class of the subsequent one.
In the first chapter, after recalling “X-ellipticity” and related concepts
introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle
for linear second order differential operators for which we only assume
a Sobolev-type inequality together with a lower terms summability. Adding
some crucial hypotheses on measure and on vector fields (Doubling property
and Poincar´e inequality), we will be able to obtain some Liouville-type results.
This chapter is based on the paper [GL03] by Guti´errez and Lanconelli.
In the second chapter we treat some ultraparabolic equations on Lie
groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results
of Cinti [Cin07] about this class of operators and associated potential theory,
we prove a scalar convexity for mean-value operators of L-subharmonic
functions, where L is our differential operator.
In the third chapter we prove a necessary and sufficient condition of regularity,
for boundary points, for Dirichlet problem on an open subset of RN related
to sub-Laplacian. On a Carnot group we give the essential background
for this type of operator, and introduce the notion of “quasi-boundedness”.
Then we show the strict relationship between this notion, the fundamental
solution of the given operator, and the regularity of the boundary points.
22
Ott, Curdin. "Optimal stopping problems for the maximum process." Thesis, University of Bath, 2013. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.601683.
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A cornerstone in the theory of optimal stopping for the maximum process is a result known as Peskir’s maximality principle. It has proved to be a powerful tool to solve optimal stopping problems involving the maximum process under the assumption that the driving process X is a time-homogeneous diffusion. In this thesis we adapt Peskir’s maximality principle to allow for X a spectrally negative L´evy processes, thereby providing a general method to approach optimal stopping problems for the maximum process driven by spectrally negative L´evy processes. We showcase this by explicitly solving three optimal stopping problems and the capped versions thereof. Here capped version means a modification of the original optimal stopping problem in the sense that the payoff is bounded from above by some constant. Moreover, we discuss applications of the aforementioned optimal stopping problems in option pricing in financial markets whose price process is driven by an exponential spectrally negative L´evy process. Finally, to further highlight the applicability of our general method, we present the solution to the problem of predicting the time at which a positive self-similar Markov process with one-sided jumps attains its maximum or minimum.
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Fournier, Frantz. "Méthodologie d'optimisation dynamique et de commande optimale des réacteurs électrochimiques discontinus." Vandoeuvre-les-Nancy, INPL, 1998. http://docnum.univ-lorraine.fr/public/INPL_T_1998_FOURNIER_F.pdf.
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Les procédés électrochimiques occupent une part non-négligeable dans l'industrie chimique. Des études préliminaires montrent cependant que le mode de fonctionnement traditionnel de ces procédés (à potentiel ou à courant constant) n'est pas toujours le meilleur. Elles encouragent à envisager l'amélioration du fonctionnement des procédés électrochimiques par l'utilisation des méthodes d'optimisation dynamique. L’étude présentée dans cette thèse propose une méthodologie de l'optimisation dynamique et de la commande optimale dans le cas des procédés électrochimiques discontinus. On cherche ainsi à formuler et résoudre les problèmes d'optimisation du fonctionnement dynamique des réacteurs électrochimiques, à analyser les différentes sensibilités des paramètres du modèle et à appliquer les profils optimaux de commande en boucle fermée dans des conditions expérimentales aussi réalistes que possibles. La méthodologie est appliquée à différents problèmes électrochimiques tels que la minimisation de la consommation d'énergie électrique, la maximisation du rendement, de la sélectivité ou encore la minimisation du temps opératoire. Toutes les méthodes d'optimisation utilisées sont fondées sur le principe du maximum. Un inventaire non exhaustif des techniques de résolution de problèmes d'optimisation dynamique et leurs principales caractéristiques sont ainsi présentées. En intégrant au problème, des contraintes physiques, ces méthodes fournissent des conditions optimales de fonctionnement réalistes. Les performances de l'optimisation dynamique sont comparées à celles résultant des meilleures conditions de fonctionnement statiques. Les améliorations entre le mode de fonctionnement optimisé et le meilleur mode usuel peuvent s'élever à plusieurs dizaine de pourcent. Différentes formes de l'analyse de la sensibilité des paramètres du modèle soulignent la validité des résultats optimaux dans des conditions opératoires qui diffèrent de celles idéalement représentée dans le modèle des réacteurs considérés. Pour la mise en œuvre de la commande optimale, des techniques de reconstruction de l'état et une loi de commande en boucle fermée ont été mis au point.
24
Li, Yusong. "Stochastic maximum principle and dynamic convex duality in continuous-time constrained portfolio optimization." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/45536.
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This thesis seeks to gain further insight into the connection between stochastic optimal control and forward and backward stochastic differential equations and its applications in solving continuous-time constrained portfolio optimization problems. Three topics are studied in this thesis. In the first part of the thesis, we focus on stochastic maximum principle, which seeks to establish the connection between stochastic optimal control and backward stochastic differential differential equations coupled with static optimality condition on the Hamiltonian. We prove a weak neccessary and sufficient maximum principle for Markovian regime switching stochastic optimal control problems. Instead of insisting on the maxi- mum condition of the Hamiltonian, we show that 0 belongs to the sum of Clarkes generalized gradient of the Hamiltonian and Clarkes normal cone of the control constraint set at the optimal control. Under a joint concavity condition on the Hamiltonian and a convexity condition on the terminal objective function, the necessary condition becomes sufficient. We give four examples to demonstrate the weak stochastic maximum principle. In the second part of the thesis, we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following the convex duality approach,we show that the necessary and sufficient optimality conditions for both the primal and dual problems can be written in terms of processes satisfying a system of FBSDEs together with other conditions. We characterise explicitly the optimal wealth and portfolio processes as functions of adjoint processes from the dual FBSDEs in a dynamic fashion and vice versa. We apply the results to solve quadratic risk minimization problems with cone-constraints and derive the explicit representations of solutions to the extended stochastic Riccati equations for such problems. In the final section of the thesis, we extend the previous result to utility maximization problems. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual problems in terms of FBSDEs plus additional conditions. Such formulation then allows us to explicitly characterize the primal optimal control as a function of the adjoint processes coming from the dual FBSDEs in a dynamic fashion and vice versa. Moreover, we also find that the optimal primal wealth process coincides with the optimal adjoint process of the dual problem and vice versa. Finally we solve three constrained utility maximization problems and contrasts the simplicity of the duality approach we propose with the technical complexity in solving the primal problem directly.
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Pesheva, Nina Christova. "A mean-field method for driven diffusive systems based on maximum entropy principle." Diss., Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/54398.
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Here, we propose a method for generating a hierarchy of mean-field approximations to study the properties of the driven diffusive Ising model at nonequilibrium steady state. In addition, the present study offers a demonstration of the practical application of the information theoretic methods to a simple interacting nonequilibrium system. The application of maximum entropy principle to the system, which is in contact with a heat reservoir, leads to a minimization principle for the generalized Helmholtz free energy. At every level of approximation the latter is expressed in terms of the corresponding mean—field variables. These play the role of variational parameters. The rate equations for the mean-field variables, which incorporate the dynamics of the system, serve as constraints to the minimization procedure.
The method is applicable to high temperatures as well to the low temperature phase coexistence regime and also has the potential for dealing with first-order phase transitions. At low temperatures the free energy is nonconvex and we use a Maxwell construction to find the relevant information for the system.
To test the method we carry out numerical calculations at the pair level of approximation for the 2-dimensional driven diffusive Ising model on a square lattice with attractive interactions. The results reproduce quite well all the basic properties of the system as reported from Monte Carlo simulations.Ph. D.
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Glickenstein, David A. "Precompactness of the Ricci flow and a maximum principle on combinatorial Yamabe flow /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2003. http://wwwlib.umi.com/cr/ucsd/fullcit?p3091326.
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Hogg, David W. (David Wardell). "The principle of maximum entropy production in a simple model of a convection cell." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/26841.
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Galise, Giulio. "Maximum principles, entire solutions and removable singularities of fully nonlinear second order equations." Doctoral thesis, Universita degli studi di Salerno, 2013. http://hdl.handle.net/10556/928.
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2011 - 2012This PhD thesis is devoted to some qualitative aspect of viscosity solutions of nonlinear second order elliptic partial di erential equations of the form F(x; u(x);Du(x);D2u(x)) = f(x)... [edited by author]
XI n.s.
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Lagache, Marc-Aurèle. "Analyse de problèmes inverses et directs en théorie du contrôle." Thesis, Toulon, 2017. http://www.theses.fr/2017TOUL0008/document.
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Le contexte général de cette thèse est l’étude de problèmes inverses et directs en théorie du contrôle. Plus précisément, les trois problèmes étudiés sont les suivants.Le premier est un problème de contrôle optimal (approche directe). Il s’agit de fournir la synthèse temps minimum du modèle cinématique d'un drone volant à altitude constante, de vitesse linéaire non nécessairement constante voulant rejoindre une trajectoire circulaire de rayon de courbure minimum.Le deuxième problème concerne une approche inverse du contrôle optimal. Il s’agit d’élaborer des méthodes théoriques de reconstruction du critère optimisé dans un problème de contrôle optimal à partir d’un ensemble de solutions à ce problème, ainsi que caractériser les "bons" ensembles de trajectoires permettant la reconstruction du critère. Le contrôle optimal inverse connait un regain d’intérêt depuis une quinzaine d’années, en particulier dans l’étude des comportements moteurs humains. En effet, selon un paradigme largement accepté en neurophysiologie, parmi tous les mouvements possibles ceux effectivement réalisés sont solutions d’un processus d’optimisation.Le troisième problème traite de stabilisation par retour de sortie. Nous analysons, à travers un exemple académique tiré du contrôle quantique, le problème de stabilisation par retour de sortie (à l’aide d’un observateur) lorsque le point où l'on souhaite stabiliser le système correspond à un contrôle qui rend le système inobservable. L’idée générale est de perturber le retour d’état stabilisant afin de garantir l’observabilité du système tout en stabilisant le système sur la cible. L’analyse de cet exemple académique nous permet dans un second temps de dégager une méthode générale pouvant s’appliquer à une classe de système beaucoup plus largeThe overall context of this thesis is the study of inverse and direct problems in control theory. More specifically, the following three problems are studied.The first one is an optimal control problem (direct approach). The aim is to give a time minimum systhesis fora kinematic model of a UAV flying at constant altitude with positive (non-necessarily constant) linear velocityin order to steer it to a fixed circle of minimum turning radius.The second problem deals with an inverse approach of optimal control. The aim is to develop theoretical methods in order to reconstruct the minimized criterion in an optimal control problem from a set of solution to this problem. The aim is also to characterize the « good » sets of trajectories leading to the reconstruction of the criterion. In the last fifteen years, there has been a renewed interest in inverse optimal control, especially inhuman motor behavior. Indeed, according to a well accepted paradigm in neurophysiology, among all possible movements, those actually accomplished are solutions of an optimization process.The third problem tackles output feedback stabilization. We analyze, via a simple academic example from quantum control, the problem of dynamic output feedback stabilization, when the point where we want to stabilize corresponds to a control value that makes the system unobservable. The general idea is to perturb the stabilizing state feedback in order to ensure the observability of the system while stabilizing it to the target.The analysis of this example allows, secondly, to identify a general procedure that can be applied to a widerclass of systems
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Bensalem, Ahmed. "Application of the discrete maximum principle to the short-term scheduling of a hydroelectric power system." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=61253.
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The purpose of this study is to develop a general algorithm to solve in a robust, flexible and fast way the short-term scheduling problems of two different multi-reservoir hydroelectric power systems. The first system consists of four reservoirs in series, the second corresponds to that of the Ste Maurice river.The solution method is based on the discrete maximum principle. Gradient method is used for the solution of the two-point boundary value problem. Two algorithms are suggested for dealing with difficulties posed by the state variable constraints. The first uses the augmented lagrangian method, the second is iterative.
Both algorithms give a satisfactory solution for the problem. However, the first requires more memory space than the second but converges more rapidly. The second algorithm has the advantage of executing an iteration in less CPU time. For large scale problems the second (iterative) algorithm option is recommended.
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Getgood, Thomas. "On the necessity of the maximum principle for systems in the proof of Hamilton's matrix Harnack inequality." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66799.
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The heat equation, while well understood in R^n , presents many novel difficulties in curved spaces. Among the techniques developed to deal with these new intricacies are differential Harnack inequalities. Beginning with the work of Li and Yau in [9] this paper will discuss the motivations and methods leading up to differential Harnack estimates culminating in Hamilton's full matrix Harnack inequality [7]. A new tool called the constant rank theorem will thereupon be developed and deployed to reprove Hamilton's result by a different route. This new proof deviates from the original substantially, but achieves the same result under the same assumptions without recourse to Hamilton's matrix maximum principle. The possible implications of this new proof are discussed in closing.L'équation de la chaleur, bien comprise dans les espaces plats, présete un certain degré de difficulté sur les variétés Riemannienne. Parmi les outils importants pour comprendre ses solutions, on trouve l'inégalité matricielle d'Hamilton [7]. Ensuite, nous présenterons un nouvel outil qui est le théorèm de rang invariable et nous l'utiliserons afin de créer une nouvelle prueve de l'inégalité matricielle d'Hamilton. Cette nouvelle prueve nous fournie le meme hypotèses mais sans avoir recours au principe du maximum pour les systèmes d'équations d'Hamilton [6]. Finalement, nous discuterons les implications potentielles de cette nouvelle technique de preuve.
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Kieri, Emil. "Accuracy aspects of the reaction-diffusion master equation on unstructured meshes." Thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-145978.
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The reaction-diffusion master equation (RDME) is a stochastic model for spatially heterogeneous chemical systems. Stochastic models have proved to be useful for problems from molecular biology since copy numbers of participating chemical species often are small, which gives a stochastic behaviour. The RDME is a discrete space model, in contrast to spatially continuous models based on Brownian motion. In this thesis two accuracy issues of the RDME on unstructured meshes are studied. The first concerns the rates of diffusion events. Errors due to previously used rates are evaluated, and a second order accurate finite volume method, not previously used in this context, is implemented. The new discretisation improves the accuracy considerably, but unfortunately it puts constraints on the mesh, limiting its current usability. The second issue concerns the rates of bimolecular reactions. Using the macroscopic reaction coefficients these rates become too low when the spatial resolution is high. Recently, two methods to overcome this problem by calculating mesoscopic reaction rates for Cartesian meshes have been proposed. The methods are compared and evaluated, and are found to work remarkably well. Their possible extension to unstructured meshes is discussed.
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Sabolová, Radka. "A study on the theoretical predictability of extreme value distributions for natural catastrophic events." Master's thesis, Vysoká škola ekonomická v Praze, 2013. http://www.nusl.cz/ntk/nusl-199590.
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The thesis deals with natural disasters from the statistical point of view and treats them as extremal observations. Basics of classical extreme value theory will be summarized and new approach based on maximum entropy principle will be proposed. Both methods will be used in order to analyze real discharge data observed at the river Vltava.
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Islam, Mohammad Mafijul. "Dose-Response Analysis for Time-Dependent Efficacy." Bowling Green State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1467295354.
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Koohkan, Mohammad Reza. "Multiscale data assimilation approaches and error characterisation applied to the inverse modelling ofatmospheric constituent emission fields." Thesis, Paris Est, 2012. http://www.theses.fr/2012PEST1140/document.
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Dans les études géophysiques, l'assimilation de données a pour but d'estimer l'état d'un système ou les paramètres d'un modèle physique de façon optimale. Pour ce faire, l'assimilation de données a besoin de trois types d'informations : des observations, un modèle physique/numérique et une description statistique de l'incertitude associée aux paramètres du système. Dans ma thèse, de nouvelles méthodes d'assimilation de données sont utilisées pour l'étude de la physico-chimie de l'atmosphère: (i) On y utilise de manière conjointe la méthode 4D-Var avec un modèle sous-maille statistique pour tenir compte des erreurs de représentativité. (ii) Des échelles multiples sont prises en compte dans la méthode d'estimation BLUE. (iii) Enfin, la méthode du maximum de vraisemblance est appliquée pour estimer des hyper-paramètres qui paramètrisent les erreurs à priori. Ces trois approches sont appliquées de manière spécifique à des problèmes de modélisation inverse des sources de polluant atmosphérique. Dans une première partie, la modélisation inverse est utilisée afin d'estimer les émissions de monoxyde de carbone sur un domaine représentant la France. Les stations du réseau d'observation considérées sont impactées par les erreurs de représentativité. Un modèle statistique sous-maille est introduit. Il est couplé au système 4D-Var afin de réduire les erreurs de représentativité. En particulier, les résultats de la modélisation inverse montrent que la méthode 4D-Var seule n'est pas adaptée pour gérer le problème de représentativité. Le système d'assimilation des données couplé conduit à une meilleure représentation de la variabilité de la concentration de CO avec une amélioration très significative des indicateurs statistiques. Dans une deuxième partie, on évalue le potentiel du réseau IMS (International Monitoring System) du CTBTO pour l'inversion d'une source accidentelle de radionucléides. Pour évaluer la performance du réseau, une grille multi-échelle adaptative pour l'espace de contrôle est optimisée selon un critère basé sur les degrés de liberté du signal (DFS). Les résultats montrent que plusieurs régions restent sous-observées par le réseau IMS. Dans la troisième et dernière partie, sont estimés les émissions de Composés Organiques Volatils (COVs) sur l'Europe de l'ouest. Cette étude d'inversion est faite sur la base des observations de 14 COVs extraites du réseau EMEP. L'évaluation des incertitudes des valeurs des inventaires d'émission et des erreurs d'observation sont faites selon le principe du maximum de vraisemblance. La distribution des inventaires d'émission a été supposée tantôt gaussienne et tantôt semi-normale. Ces deux hypothèses sont appliquées pour inverser le champs des inventaires d'émission. Les résultats de ces deux approches sont comparés. Bien que la correction apportée sur les inventaires est plus forte avec l'hypothèse Gaussienne que semi-normale, les indicateurs statistiques montrent que l'hypothèse de la distribution semi-normale donne de meilleurs résultats de concentrations que celle GaussienneData assimilation in geophysical sciences aims at optimally estimating the state of the system or some parameters of the system's physical model. To do so, data assimilation needs three types of information: observations and background information, a physical/numerical model, and some statistical description that prescribes uncertainties to each componenent of the system.In my dissertation, new methodologies of data assimilation are used in atmospheric chemistry and physics: the joint use of a 4D-Var with a subgrid statistical model to consistently account for representativeness errors, accounting for multiple scale in the BLUE estimation principle, and a better estimation of prior errors using objective estimation of hyperparameters. These three approaches will be specifically applied to inverse modelling problems focussing on the emission fields of tracers or pollutants. First, in order to estimate the emission inventories of carbon monoxide over France, in-situ stations which are impacted by the representativeness errors are used. A subgrid model is introduced and coupled with a 4D-Var to reduce the representativeness error. Indeed, the results of inverse modelling showed that the 4D-Var routine was not fit to handle the representativeness issues. The coupled data assimilation system led to a much better representation of theCO concentration variability, with a significant improvement of statistical indicators, and more consistent estimation of the CO emission inventory. Second, the evaluation of the potential of the IMS (International Monitoring System) radionuclide network is performed for the inversion of an accidental source. In order to assess the performance of the global network, a multiscale adaptive grid is optimised using a criterion based on degrees of freedom for the signal (DFS). The results show that several specific regions remain poorly observed by the IMS network. Finally, the inversion of the surface fluxes of Volatile Organic Compounds (VOC) are carried out over Western Europe using EMEP stations. The uncertainties of the background values of the emissions, as well as the covariance matrix of the observation errors, are estimated according to the maximum likelihood principle. The prior probability density function of the control parameters is chosen to be Gaussian or semi-normal distributed. Grid-size emission inventories are inverted under these two statistical assumptions. The two kinds of approaches are compared. With the Gaussian assumption, the departure between the posterior and the prior emission inventories is higher than when using the semi-normal assumption, but that method does not provide better scores than the semi-normal in a forecast experiment
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Fontaine, Clément. "Supervision optimale des véhicules électriques hybrides en présence de contraintes sur l’état." Thesis, Valenciennes, 2013. http://www.theses.fr/2013VALE0024.
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La propulsion des véhicules électriques hybrides parallèles est généralement assurée par un moteur à combustion interne combiné à une machine électrique réversible. Les flux de puissance entre ces deux organes de traction sont déterminés par un algorithme de supervision, qui vise à réduire la consommation de carburant et éventuellement les émissions de certains polluants. Dans la littérature, la théorie de la commande optimale est maintenant reconnue comme étant un cadre puissant pour l’élaboration de lois de commande pour la gestion énergétique des véhicules full-hybrides. Ces stratégies, dénommée « Stratégies de Minimisation de la Consommation Equivalente » (ECMS) sont basée sur le principe du Maximum de Pontryagin. Pour démontrer l’optimalité de l’ECMS, on doit supposer que les limites du système de stockage ne sont pas atteintes durant le cycle de conduite. Il n’est plus possible de faire cette hypothèse lorsque l’on considère les véhicules micro et mild hybrides étudiés dans cette thèse car la variable d’état atteint généralement plusieurs fois les bornes. Des outils mathématiques adaptés à l’étude des problèmes de commande avec contraintes sur l’état sont présentés et appliqués à deux problèmes en lien avec la gestion énergétique. Le premier problème consiste à déterminer le profil optimal de la tension aux bornes d’un pack d’ultra-capacités. Le second problème se concentre sur un système électrique intégrant deux stockeurs. L’accent est mis sur l’étude des conditions d’optimalités valables lorsque les contraintes sur l’état sont actives. Les conséquences de ces conditions pour la commande en ligne sont mises en avant et exploitées afin de concevoir une commande en temps réel. Les performances sont évaluées à l’aide d’un prototype. Une comparaison avec une approche de type ECMS plus classique est également présentéeParallel hybrid electric vehicles are generally propelled by an internal combustion engine, which is combined to a reversible electric machine. The power flows between these two traction devices are determined by a supervisory control algorithm, which aims at reducing the fuel consumption and possibly some polluting emissions. In the literature, optimal control theory is now recognized as a powerful framework for the synthesis of energy management strategies for full hybrid vehicles. These strategies are referred to as “Equivalent Consumption Minimization Strategies” (ECMS) and are based on the Pontryagin Maximum Principle. To demonstrate the optimality of ECMS, it must be assumed that the storage system limits are not reached during the drive cycle. This hypothesis cannot be made anymore when considering the micro and mild hybrid vehicles studied in this thesis because the state variable generally reaches several times the boundaries. Some mathematical tools suitable for the study of state constrained optimal control problems are introduced and applied to two energy management problems. The first problem consists in determining the optimal profile of the voltage across a pack of ultra-capacitors. The second problem focuses on a dual storage system. The stress is put on the study of the optimality conditions holding in case of active state constraints. Some consequences of these conditions for the online control are pointed out are exploited for the design of a real-time controller. Its performances are assessed using a demonstrator vehicle. A comparison with a classical ECMS-based approach is also provided
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Bourdin, Loïc. "Contributions au calcul des variations et au principe du maximum de Pontryagin en calculs time scale et fractionnaire." Thesis, Pau, 2013. http://www.theses.fr/2013PAUU3009/document.
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Cette thèse est une contribution au calcul des variations et à la théorie du contrôle optimal dans les cadres discret, plus généralement time scale, et fractionnaire. Ces deux domaines ont récemment connu un développement considérable dû pour l’un à son application en informatique et pour l’autre à son essor dans des problèmes physiques de diffusion anormale. Que ce soit dans le cadre time scale ou dans le cadre fractionnaire, nos objectifs sont de : a) développer un calcul des variations et étendre quelques résultats classiques (voir plus bas); b) établir un principe du maximum de Pontryagin (PMP en abrégé) pour des problèmes de contrôle optimal. Dans ce but, nous généralisons plusieurs méthodes variationnelles usuelles, allant du simple calcul des variations au principe variationnel d’Ekeland (couplé avec la technique des variations-aiguilles), en passant par l’étude d’invariances variationnelles par des groupes de transformations. Les démonstrations des PMPs nous amènent également à employer des théorèmes de point fixe et à prendre en considération la technique des multiplicateurs de Lagrange ou encore une méthode basée sur un théorème d’inversion locale conique. Ce manuscrit est donc composé de deux parties : la Partie 1 traite de problèmes variationnels posés sur time scale et la Partie 2 est consacrée à leurs pendants fractionnaires. Dans chacune de ces deux parties, nous suivons l’organisation suivante : 1. détermination de l’équation d’Euler-Lagrange caractérisant les points critiques d’une fonctionnelle Lagrangienne ; 2. énoncé d’un théorème de type Noether assurant l’existence d’une constante de mouvement pour les équations d’Euler-Lagrange admettant une symétrie ; 3. énoncé d’un théorème de type Tonelli assurant l’existence d’un minimiseur pour une fonctionnelle Lagrangienne et donc, par la même occasion, d’une solution pour l’équation d’Euler-Lagrange associée (uniquement en Partie 2) ; 4. énoncé d’un PMP (version forte en Partie 1, version faible en Partie 2) donnant une condition nécessaire pour les trajectoires qui sont solutions de problèmes de contrôle optimal généraux non-linéaires ; 5. détermination d’une condition de type Helmholtz caractérisant les équations provenant d’un calcul des variations (uniquement en Partie 1 et uniquement dans les cas purement continu et purement discret). Des théorèmes de type Cauchy-Lipschitz nécessaires à l’étude de problèmes de contrôle optimal sont démontrés en AnnexeThis dissertation deals with the mathematical fields called calculus of variations and optimal control theory. More precisely, we develop some aspects of these two domains in discrete, more generally time scale, and fractional frameworks. Indeed, these two settings have recently experience a significant development due to its applications in computing for the first one and to its emergence in physical contexts of anomalous diffusion for the second one. In both frameworks, our goals are: a) to develop a calculus of variations and extend some classical results (see below); b) to state a Pontryagin maximum principle (denoted in short PMP) for optimal control problems. Towards these purposes, we generalize several classical variational methods, including the Ekeland’s variational principle (combined with needle-like variations) as well as variational invariances via the action of groups of transformations. Furthermore, the investigations for PMPs lead us to use fixed point theorems and to consider the Lagrange multiplier technique and a method based on a conic implicit function theorem. This manuscript is made up of two parts : Part A deals with variational problems on time scale and Part B is devoted to their fractional analogues. In each of these parts, we follow (with minor differences) the following organization: 1. obtaining of an Euler-Lagrange equation characterizing the critical points of a Lagrangian functional; 2. statement of a Noether-type theorem ensuring the existence of a constant of motion for Euler-Lagrange equations admitting a symmetry;3. statement of a Tonelli-type theorem ensuring the existence of a minimizer for a Lagrangian functional and, consequently, of a solution for the corresponding Euler-Lagrange equation (only in Part B); 4. statement of a PMP (strong version in Part A and weak version in Part B) giving a necessary condition for the solutions of general nonlinear optimal control problems; 5. obtaining of a Helmholtz condition characterizing the equations deriving from a calculus of variations (only in Part A and only in the purely continuous and purely discrete cases). Some Picard-Lindelöf type theorems necessary for the analysis of optimal control problems are obtained in Appendices
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JÃnior, Elzon CÃzar Bezerra. "Um estudo sobre regularidade de soluÃÃes de equaÃÃes diferenciais parciais elÃpticas." Universidade Federal do CearÃ, 2016. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17187.
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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgicoO objetivo principal deste trabalho à o estudo da regularidade de soluÃÃes de equaÃÃes diferenciais parciais elÃpticas de segunda ordem, serÃo usadas tÃcnicas tais como o princÃpio do mÃximo, estimativas a priori e a desigualdade de Harnack. Por fim generalizamos o conceito de soluÃÃo buscando soluÃÃes no espaÃo de Sobolev W2,p(Ω).
The main objective of this work is to study the regularity of solutions of elliptic partial differential equations of second order, will be used techniques such as the principle of maximum estimates a priori and the unequal Harnack. Finally generalize the solution concept seeking solutions in the Sobolev space W2,p((Ω).
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Kalauch, Anke. "Positive-off-diagonal Operators on Ordered Normed Spaces and Maximum Principles for M-Operators." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2007. http://nbn-resolving.de/urn:nbn:de:swb:14-1169822895129-71711.
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M-matrices are extensively employed in numerical analysis. These matrices can be generalized by corresponding operators on a partially ordered normed space. We extend results which are well-known for M-matrices to this more general setting. We investigate two different notions of an M-operator, where we focus on two questions: 1. For which types of partially ordered normed spaces do the both notions coincide? This leads to the study of positive-off-diagonal operators. 2. Which conditions on an M-operator ensure that its (positive) inverse satisfies certain maximum principles? We deal with generalizations of the "maximum principle for inverse column entries"M-Matrizen werden in der numerischen Mathematik vielfältig angewandt. Eine Verallgemeinerung dieser Matrizen sind entsprechende Operatoren auf halbgeordneten normierten Räumen. Bekannte Aussagen aus der Theorie der M-Matrizen werden auf diese Situation übertragen. Für zwei verschiedene Typen von M-Operatoren werden die folgenden Fragen behandelt: 1. Für welche geordneten normierten Räume sind die beiden Typen gleich? Dies führt zur Untersuchung außerdiagonal-positiver Operatoren. 2. Welche Bedingungen an einen M-Operator sichern, dass seine (positive) Inverse gewissen Maximumprinzipien genügt? Es werden Verallgemeinerungen des "Maximumprinzips für inverse Spalteneinträge" angegeben und untersucht
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Fowler, Philip, and Pernilla Lindblad. "The Minimum Description Length principle in model selection : An evaluation of the renormalized maximum likelihood criterion in linear- and logistic regression analysis." Thesis, Umeå universitet, Statistiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-49707.
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Fu, Guanxing [Verfasser], Ulrich [Gutachter] Horst, Jean-Pierre [Gutachter] Fouque, and Huyen [Gutachter] Pham. "Maximum Principle for Reflected BSPDE and Mean Field Game Theory with Applications / Guanxing Fu ; Gutachter: Ulrich Horst, Jean-Pierre Fouque, Huyen Pham." Berlin : Humboldt-Universität zu Berlin, 2018. http://d-nb.info/1185665641/34.
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Evans, Lawrence C. 1949. "A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/59784.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 125-126).
This thesis consists of two results. The first result is a strong maximum principle for certain parabolic systems of equations, which, for illustrative purposes, I consider as reaction-diffusion systems. Using the theory of viscosity solutions, I give a proof which extends the previous theorem to no longer require any regularity assumptions on the boundary of the convex set in which the system takes its values. The second result is an approximation scheme for reflected stochastic differential equations (SDE) of the Stratonovich type. This is a joint result with Professor Daniel W. Stroock. We show that the distribution of the solution to such a reflected SDE is the weak limit of the distribution of the solutions of the reflected SDEs one gets by replacing the driving Brownian motion by its N-dyadic linear interpolation. In particular, we can infer geometric properties of the solutions to a Stratonovich reflected SDE from those of the solutions to the approximating reflected SDE.
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Kalauch, Anke. "Positive-off-diagonal Operators on Ordered Normed Spaces and Maximum Principles for M-Operators." Doctoral thesis, Technische Universität Dresden, 2006. https://tud.qucosa.de/id/qucosa%3A25013.
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M-matrices are extensively employed in numerical analysis. These matrices can be generalized by corresponding operators on a partially ordered normed space. We extend results which are well-known for M-matrices to this more general setting. We investigate two different notions of an M-operator, where we focus on two questions: 1. For which types of partially ordered normed spaces do the both notions coincide? This leads to the study of positive-off-diagonal operators. 2. Which conditions on an M-operator ensure that its (positive) inverse satisfies certain maximum principles? We deal with generalizations of the "maximum principle for inverse column entries".M-Matrizen werden in der numerischen Mathematik vielfältig angewandt. Eine Verallgemeinerung dieser Matrizen sind entsprechende Operatoren auf halbgeordneten normierten Räumen. Bekannte Aussagen aus der Theorie der M-Matrizen werden auf diese Situation übertragen. Für zwei verschiedene Typen von M-Operatoren werden die folgenden Fragen behandelt: 1. Für welche geordneten normierten Räume sind die beiden Typen gleich? Dies führt zur Untersuchung außerdiagonal-positiver Operatoren. 2. Welche Bedingungen an einen M-Operator sichern, dass seine (positive) Inverse gewissen Maximumprinzipien genügt? Es werden Verallgemeinerungen des "Maximumprinzips für inverse Spalteneinträge" angegeben und untersucht.
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Daghighi, Abtin. "Regularity and uniqueness-related properties of solutions with respect to locally integrable structures." Doctoral thesis, Mittuniversitetet, Avdelningen för ämnesdidaktik och matematik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-21641.
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We prove that a smooth generic embedded CR submanifold of C^n obeys the maximum principle for continuous CR functions if and only if it is weakly 1-concave. The proof of the maximum principle in the original manuscript has later been generalized to embedded weakly q-concave CR submanifolds of certain complex manifolds. We give a generalization of a known result regarding automatic smoothness of solutions to the homogeneous problem for the tangential CR vector fields given local holomorphic extension. This generalization ensures that a given locally integrable structure is hypocomplex at the origin if and only if it does not allow solutions near the origin which cannot be represented by a smooth function near the origin. We give a sufficient condition under which it holds true that if a smooth CR function f on a smooth generic embedded CR submanifold, M, of C^n, vanishes to infinite order along a C^infty-smooth curve \gamma in M, then f vanishes on an M-neighborhood of \gamma. We prove a local maximum principle for certain locally integrable structures.Funding by FMB, based at Uppsala University.
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Taylor, Tracy A. "Optimal Control and Its Application to the Life-Cycle Savings Problem." VCU Scholars Compass, 2016. http://scholarscompass.vcu.edu/etd/4288.
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Throughout the course of this thesis, we give an introduction to optimal control theory and its necessary conditions, prove Pontryagin's Maximum Principle, and present the life-cycle saving under uncertain lifetime optimal control problem. We present a very involved sensitivity analysis that determines how a change in the initial wealth, discount factor, or relative risk aversion coefficient may affect the model the terminal depletion of wealth time, optimal consumption path, and optimal accumulation of wealth path. Through simulation of the life-cycle saving under uncertain lifetime model, we are not only able to present the model dynamics through time, but also to demonstrate the feasibility of the model.
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Junker, Philipp [Verfasser], Klaus [Gutachter] Hackl, and Alexander [Gutachter] Hartmaier. "Simulation of shape memory alloys : material modeling using the principle of maximum dissipation / Philipp Junker ; Gutachter: Klaus Hackl, Alexander Hartmaier ; Fakultät für Maschinenbau." Bochum : Ruhr-Universität Bochum, 2012. http://d-nb.info/1226426360/34.
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Chakir, El-Alaoui El-Houcine. "Les métriques sous riemanniennes en dimension 3." Rouen, 1996. http://www.theses.fr/1996ROUES055.
Full textAbstract:
Cette thèse est consacrée essentiellement à l'étude des métriques sous-riemanniennes dites de contact en dimension 3. Bien que cette étude soit faite localement, on observe des différences fondamentales avec les métriques riemanniennes. En particulier, les lieux conjugue et cut d'un point p contiennent p dans leur adhérence. Ce travail se divise en deux parties : 1. On montre, dans un premier temps, qu'on peut associer à toute métrique sous-riemannienne de contact formelle une forme normale formelle. Ensuite, dans un deuxième temps, on montre que cette forme normale est actuellement lisse (i. E. C, c) si la métrique l'est. Aussi, cette forme normale permet de définir des invariants associés aux métriques sous-riemanniennes de contact. 2. A l'aide de cette forme normale on prouve que l'application exponentielle d'une métrique sous-riemannienne de contact générique est déterminée par un certain jet fini de la métrique. Et on en déduit une classification générique de ces singularités (i. E. Lieux conjugués).
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Coco, Marco. "Monte Carlo study of charge and phonon transport in graphene." Doctoral thesis, Università di Catania, 2017. http://hdl.handle.net/10761/3811.
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In this thesis, we investigate charge transport in graphene. Graphene is one of the most important new materials with a wide range of properties, rarely together in the same material, and it is the ideal candidate for future electronic devices. The dynamics of electrons in the conduction band is analyzed, by considering values of Fermi levels high enough to neglect the dynamics in the valence band. This is equivalent to a n-type doping for traditional semiconductors.
Degeneracy effects are very important in graphene and then it becomes mandatory to consistently include the Pauli exclusion principle.
We develop a new Direct Simulation Monte Carlo (DSMC) procedure to solve the Boltzmann transport equation, that properly takes into account the Pauli principle. For a cross-validation of the results, we also solve the Boltzmann equation in a deterministic way by using the Discontinuous Galerkin method. The agreement of the results is excellent. A comparison of the new DSMC results with those obtained by means of well established hydrodynamical models are presented as well, and again the agreement is very good.
This new approach is applied to study the transport properties in suspended monolayer graphene and then in a layer of graphene on different substrates, obtaining the expected results as the degradation of mobilities.
Regarding phonon transport, we investigate the thermal effects in a suspended monolayer graphene due to the charge flow under an applied electric field. A complete model is considered, with all the phonon branches, both in-plane and out of plane ones. Moreover, we describe the phonon populations without any approximation of the distribution with an equivalent Bose-Einstein one. The distribution is built by means of the intermediate results arising from the new DSMC, by counting the number of the emission and absorption processes due to the interaction between electrons and phonons. The phonon-phonon interaction is treated in a standard way with a BGK approximation.
We are able to determine the increase of the temperature due to the charge flow and to predict its raise for any values of electric fields and Fermi energies. Moreover, it is shown that the inclusion of a complete phonon model leads to a lower heating effect with respect to other simplified models.
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Sushanta, Mitra. "Breakup Process of Plane Liquid Sheets and Prediction of Initial Droplet Size and Velocity Distributions in Sprays." Thesis, University of Waterloo, 2001. http://hdl.handle.net/10012/931.
Full textAbstract:
Spray models are increasingly becoming the principal tools in the design and development of gas turbine combustors. Spray modeling requires a knowledge of the liquid atomization process, and the sizes and velocities of subsequently formed droplets as initial conditions. In order to have a better understanding of the liquid atomization process,the breakup characteristics of plane liquid sheets in co-flowing gas streams are investigated by means of linear and nonlinear hydrodynamic instability analyses. The liquid sheet breakup process is studied for initial sinuous and varicose modes of disturbance. It is observed that the sheet breakup occurs at half-wavelength intervals for an initial sinuous disturbance and at full-wavelength intervals for an initial varicose disturbance. It is also found that under certain operating conditions, the breakup process is dictated by the initial varicose disturbance compare to its sinuous counterpart. Further, the breakup process is studied for the combined mode and it is found that the sheet breakup occurs at half- or full-wavelength intervals depending on the proportion of the individual sinuous and varicose disturbances. In general, the breakup length decreases with the increase in the Weber number, gas-to-liquid velocity and density ratios. A predictive model of the initial droplet size and velocity distributions for the subsequently formed spray is also formulated here. The present model incorporates the deterministic aspect of spray formation by calculating the breakup length and the mass-mean diameter and the stochastic aspect by statistical means through the maximum entropy principle based on Bayesian entropy. The two sub-models are coupled together by the various source terms signifying the liquid-gas interaction and a prior distribution based on instability analysis, which provides information regarding the unstable wave elements on the two liquid-gas interfaces. Experimental investigation of the breakup characteristics of the liquid sheet is performed by a high speed CCD camera and the measurement of the initial droplet size and distributions is conducted by phase-Doppler interferometry. Good agreement of the theoretical breakup length with the experiment is obtained for a planar, an annular and a gas turbine nozzle. The predicted initial droplet size and velocity distributions show reasonably satisfactory agreement with experimental data for all the three types of nozzles. Hence this spray model can be utilized to predict the initial droplet size and velocity distributions in sprays, which can then be implemented as a front-end subroutine to the existing computer codes.
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Berkessa, Zewude Alemayehu. "Problém energeticky optimální jízdy vlaku." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-401555.
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The Diploma thesis deals with the problem of energy-efficient train control. It presents the basic survey of mathematical models used in the problem of energy-efficient train control, analysis of optimal driving regimes, determining optimal switching times between optimal driving regimes and timetabling of the train. The mathematical formulation of the problem is done using Newton's second law of motion and other known physical laws. To analyse optimal driving regimes and determine the switching times between optimal driving regimes, we apply tools of optimal control theory, particularly Pontryagin's Maximum Principle. The timetabling of the train is discussed from the numerical solution of the settled non-linear programming problem.