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Dissertations / Theses on the topic 'Linear singularly perturbed problem'

Author: Grafiati

Published: 3 June 2025

Last updated: 19 July 2025

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1

Howe, Sei. "Upper and lower bounds for singularly perturbed linear quadratic optimal control problems." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/54758.

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The question of how to optimally control a large scale system is widely considered to be difficult to solve due to the size of the problem. This difficulty is further compounded when a system exhibits a two time-scale structure where some components evolve slowly and others evolve quickly. When this occurs, the optimal control problem is regarded as singularly perturbed with a perturbation parameter epsilon representing the ratio of the slow time-scale to the fast time-scale. As epsilon goes to zero, the system becomes stiff resulting in a computationally intractable problem. In this thesis, w

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2

Tang, Ying. "Stability analysis and Tikhonov approximation for linear singularly perturbed hyperbolic systems." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAT054/document.

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Les dynamiques des systèmes modélisés par des équations aux dérivées partielles (EDPs) en dimension infinie sont largement liées aux réseaux physiques. La synthèse de la commande et l'analyse de la stabilité de ces systèmes sont étudiées dans cette thèse. Les systèmes singulièrement perturbés, contenant des échelles de temps multiples sont naturels dans les systèmes physiques avec des petits paramètres parasitaires, généralement de petites constantes de temps, les masses, les inductances, les moments d'inertie. La théorie des perturbations singulières a été introduite pour le contrôle à la fin

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3

Kunert, Gerd. "A note on the energy norm for a singularly perturbed model problem." Universitätsbibliothek Chemnitz, 2001. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200100062.

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A singularly perturbed reaction-diffusion model problem is considered, and the choice of an appropriate norm is discussed. Particular emphasis is given to the energy norm. Certain prejudices against this norm are investigated and disproved. Moreover, an adaptive finite element algorithm is presented which exhibits an optimal error decrease in the energy norm in some simple numerical experiments. This underlines the suitability of the energy norm.

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4

Adkins, Jacob. "A Robust Numerical Method for a Singularly Perturbed Nonlinear Initial Value Problem." Kent State University Honors College / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ksuhonors1513331499579714.

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5

Kunert, Gerd. "Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes." Universitätsbibliothek Chemnitz, 2001. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200100011.

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Singularly perturbed problems often yield solutions ith strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction-diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite element meshes. The estimator is based on the solution of a local problem, and yields error bounds uniformly

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6

Grosman, Serguei. "Robust local problem error estimation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600475.

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Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, e.g. strong boundary and/or interior layers. This anisotropy is reflected in the discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the a posteriori error estimator with respect to both the perturbation parameters of the problem and the anisotropy of the mesh. An estimator that has shown to be one of the most reliable for reaction-diffusion problem is the <i>equilibrated residual method</i> and its modification done by

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7

Blomberg, Magnus. "High Bandwidth Control of a Small Aerial Vehicle." Thesis, Linköpings universitet, Reglerteknik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-119622.

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Small aerial vehicles such as quad-rotors have been widely used commercially, for research and for hobby for the last decade with use still growing. The high interest is mainly due to the vehicles being small, simple, cheap and versatile. Among rigid body dynamics fast dynamics exist cohering to motors and other fast actuators. A linear quadratic control design technique is here investigated. The design technique suggests that the linear quadratic controller can be designed with penalties on the slow states only. The fast dynamics are modeled but the states are not penalised in the linear quad

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8

Dalla, Riva Matteo. "Potential theoretic methods for the analysis of singularly perturbed problems in linearized elasticity." Doctoral thesis, Università degli studi di Padova, 2008. http://hdl.handle.net/11577/3426270.

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The dissertation is made of two chapters. The first chapter is dedicated to the investigation of some properties of the layer potentials of a constant coefficient elliptic partial differential operator. In the second chapter, we focus our attention to the Lamè equations, which are related to the physic of an isotropic homogeneous elastic body. In particular, in the first chapter, we investigate the dependence of the single layer potential upon perturbation of the density, the support and the coefficients of the corresponding operator. Under some more restrictive assumptions on the operator,

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9

Kunert, Gerd. "A posteriori H^1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes." Universitätsbibliothek Chemnitz, 2001. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200100730.

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The paper deals with a singularly perturbed reaction diffusion model problem. The focus is on reliable a posteriori error estimators for the H^1 seminorm that can be applied to anisotropic finite element meshes. A residual error estimator and a local problem error estimator are proposed and rigorously analysed. They are locally equivalent, and both bound the error reliably. Furthermore three modifications of these estimators are introduced and discussed. Numerical experiments for all estimators complement and confirm the theoretical results.

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10

Maddah, Sumayya Suzy. "Formal reduction of differential systems : Singularly-perturbed linear differential systems and completely integrable Pfaffian systems with normal crossings." Thesis, Limoges, 2015. http://www.theses.fr/2015LIMO0065/document.

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Dans cette thèse, nous nous sommes intéressés à l'analyse locale de systèmes différentiels linéaires singulièrement perturbés et de systèmes de Pfaff complètement intégrables et multivariés à croisements normaux. De tels systèmes ont une vaste littérature et se retrouvent dans de nombreuses applications. Cependant, leur résolution symbolique est toujours à l'étude. Nos approches reposent sur l'état de l'art de la réduction formelle des systèmes linéaires singuliers d'équations différentielles ordinaires univariées (ODS). Dans le cas des systèmes différentiels linéaires singulièrement perturbés

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11

Kunert, Gerd. "Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes." Universitätsbibliothek Chemnitz, 2000. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200000867.

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We consider a singularly perturbed reaction-diffusion problem and derive and rigorously analyse an a posteriori residual error estimator that can be applied to anisotropic finite element meshes. The quotient of the upper and lower error bounds is the so-called matching function which depends on the anisotropy (of the mesh and the solution) but not on the small perturbation parameter. This matching function measures how well the anisotropic finite element mesh corresponds to the anisotropic problem. Provided this correspondence is sufficiently good, the matching function is O(1). Hence one obt

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12

Kunert, Gerd. "A posteriori error estimation for convection dominated problems on anisotropic meshes." Universitätsbibliothek Chemnitz, 2002. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200200255.

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A singularly perturbed convection-diffusion problem in two and three space dimensions is discretized using the streamline upwind Petrov Galerkin (SUPG) variant of the finite element method. The dominant convection frequently gives rise to solutions with layers; hence anisotropic finite elements can be applied advantageously. The main focus is on a posteriori energy norm error estimation that is robust in the perturbation parameter and with respect to the mesh anisotropy. A residual error estimator and a local problem error estimator are proposed and investigated. The analysis reveals that th

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13

Abate, Domenico. "Modelling and control of RFX-mod tokamak equilibria." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3421955.

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The subject that concerns this thesis is the modelling and control of plasma equilibria in the RFX-mod device operating as shaped tokamak. The aim was to develop an overall model of the plasma-conductors-controller system of RFX-mod shaped tokamak configuration for electromagnetic control purposes, with particular focus on vertical stability. Thus, the RFX-mod device is described by models of increasing complexity and involving both theoretical and experimental data. The CREATE-L code is used to develop 2D linearized plasma response models, with simplifying assumptions on the conducting struct

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14

"Concentration phenomena for a singularly perturbed Neumann problem." 2010. http://library.cuhk.edu.hk/record=b5894428.

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Ao, Weiwei.<br>"August 2010."<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.<br>Includes bibliographical references (leaves 92-97).<br>Abstracts in English and Chinese.<br>Abstract --- p.ii<br>Acknowledgement --- p.v<br>Chapter 1 --- Introduction --- p.1<br>Chapter 2 --- Spikes on Single Line-Segments --- p.12<br>Chapter 2.1 --- Ansatz and sketch of the proof --- p.12<br>Chapter 2.2 --- Linear theory --- p.15<br>Chapter 2.3 --- The non linear projected problem --- p.20<br>Chapter 2.4 --- Projection of the error and proof of Theorem 1.0.1 --- p.24<br>Chapter 3 --- The tripl

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15

"Multiple nodal solutions for some singularly perturbed Neumann problems." 2004. http://library.cuhk.edu.hk/record=b5892097.

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Chan Sik Kin.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.<br>Includes bibliographical references (leaves 38-41).<br>Abstracts in English and Chinese.<br>Chapter 1 --- Introduction --- p.4<br>Chapter 2 --- Preliminary analysis --- p.11<br>Chapter 3 --- Liapunov-Schmidt Reduction --- p.19<br>Chapter 4 --- The reduced problem: A Minimizing Procedure --- p.32<br>Chapter 5 --- Proof of the theorem 1.2 --- p.35<br>Bibliography --- p.38

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16

"An algebraic approach to time scale analysis of singularly perturbed linear systems." Laboratory for Information and Decision Systems, Massachusetts Institute of Technology], 1986. http://hdl.handle.net/1721.1/2957.

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Xi-Cheng Lou, Alan S. Willsky, George C. Verghese.<br>Bibliography: p. 41.<br>Supported by the Air Force Office of Scientific Research under grant AFOSR-82-0258 Supported by the Army Research Offcie under grant DAAG-29-84-K-005

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17

"A higher-order energy expansion to two-dimensional singularly perturbed Neumann problems." 2004. http://library.cuhk.edu.hk/record=b5891877.

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Yeung Wai Kong.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.<br>Includes bibliographical references (leaves 51-55).<br>Abstracts in English and Chinese.<br>Chapter 1 --- Introduction --- p.5<br>Chapter 2 --- Some Preliminaries --- p.13<br>Chapter 3 --- "Approximate Function we,p" --- p.17<br>Chapter 4 --- "The Computation Of Je[we,p]" --- p.21<br>Chapter 5 --- The Signs of c1 And c3 --- p.30<br>Chapter 6 --- The Asymptotic Behavior of ue and Je[ue] --- p.35<br>Chapter 7 --- "The Proofs Of Theorem 1.1, Theorem 1.2 And Corol- lary 11" --- p.40<br>Appendix --- p.43<br>Bibli

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18

Chen, Ching-Fa, and 陳清發. "Some Aspects on Robust Stability of Uncertain Linear Singularly Perturbed Systems with Multiple Time Delays." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/83794292303530471484.

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19

Yang, Zi-Yi, and 楊子儀. "Linear Quadratic Nash Game Based Tracker for Multiparameter Singularly Perturbed Sampled-data Systems:Digital Redesign Approach." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/32562852160032278021.

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碩士<br>國立成功大學<br>電機工程學系碩博士班<br>94<br>In this thesis, a tracker for the linear quadratic Nash game of multiparameter singularly perturbed sampled-data systems is newly established. A generalized cross-coupled multiparameter algebraic Riccati equation (GCMARE) for two quadratic cost functions is needed to be solved by applying the LQR design methodology for the tracker design. Firstly, the asymptotic expansions for the GCMARE are newly established, and the proposed algorithm based on the Newton’s method for solving the GCMARE guarantees the quadratic convergence. Then the low-gain sample-data con

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