Download or read book Interior penalty approximation for optimal control problems Optimality conditions in stochastic optimal control theory written by Francisco Jose Silva and published by . This book was released on 2010 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Résumé français : Cette thèse est divisée en deux parties. Dans la première partie on s'intéresse aux problèmes de commande optimale déterministes et on étudie des approximations intérieures pour deux problèmes modèles avec des contraintes de non-négativité sur la commande. Le premier modèle est un problème de commande optimale dont la fonction de coût est quadratique et dont la dynamique est régie par une équation différentielle ordinaire. Pour une classe générale de fonctions de pénalité intérieure, on montre comment calculer le terme principal du développement ponctuel de l'état et de l'état adjoint. Notre argument principal se fonde sur le fait suivant: si la commande optimale pour le problème initial satisfait les conditions de complémentarité stricte pour le Hamiltonien sauf en un nombre fini d'instants, les estimations pour le problème de commande optimale pénalisé peuvent être obtenues à partir des estimations pour un problème stationnaire associé. Nos résultats fournissent plusieurs types de mesures de qualité de l'approximation pour la technique de pénalisation: estimations des erreurs de la commande , estimations des erreurs pour l'état et l'état adjoint et aussi estimations de erreurs pour la fonction valeur. Le second modèle est le problème de commande optimale d'une équation semi-linéaire elliptique avec conditions de Dirichlet homogène au bord, la commande étant distribuée sur le domaine et positive. L'approche est la même que pour le premier modèle, c'est-à-dire que l'on considère une famille de problèmes pénalisés, dont la solution définit une trajectoire centrale qui converge vers la solution du problème initial. De cette manière, on peut étendre les résultats, obtenus dans le cadre d'équations différentielles, au contrôle optimal d'équations elliptiques semi-linéaires. Dans la deuxième partie on s'intéresse aux problèmes de commande optimale stochastiques. Dans un premier temps, on considère un problème linéaire quadratique stochastique avec des contraintes de non-negativité sur la commande et on étend les estimations d'erreur pour l'approximation par pénalisation logarithmique. La preuve s'appuie sur le principe de Pontriaguine stochastique et un argument de dualité. Ensuite, on considère un problème de commande stochastique général avec des contraintes convexes sur la commande. L'approche dite variationnelle nous permet d'obtenir un développement au premier et au second ordre pour l'état et la fonction de coût, autour d'un minimum local. Avec ces développements on peut montrer des conditions générales d'optimalité de premier ordre et, sous une hypothèse géométrique sur l'ensemble des contraintes, des conditions nécessaires du second ordre sont aussi établies.
Download or read book Global Methods in Optimal Control Theory written by Vadim Krotov and published by CRC Press. This book was released on 1995-10-13 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work describes all basic equaitons and inequalities that form the necessary and sufficient optimality conditions of variational calculus and the theory of optimal control. Subjects addressed include developments in the investigation of optimality conditions, new classes of solutions, analytical and computation methods, and applications.
Download or read book Deterministic and Stochastic Optimal Control and Inverse Problems written by Baasansuren Jadamba and published by CRC Press. This book was released on 2021-12-15 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems of identifying parameters and initial/boundary conditions in deterministic and stochastic partial differential equations constitute a vibrant and emerging research area that has found numerous applications. A related problem of paramount importance is the optimal control problem for stochastic differential equations. This edited volume comprises invited contributions from world-renowned researchers in the subject of control and inverse problems. There are several contributions on optimal control and inverse problems covering different aspects of the theory, numerical methods, and applications. Besides a unified presentation of the most recent and relevant developments, this volume also presents some survey articles to make the material self-contained. To maintain the highest level of scientific quality, all manuscripts have been thoroughly reviewed.
Download or read book Structure of Approximate Solutions of Optimal Control Problems written by Alexander J. Zaslavski and published by Springer Science & Business Media. This book was released on 2013-08-04 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title examines the structure of approximate solutions of optimal control problems considered on subintervals of a real line. Specifically at the properties of approximate solutions which are independent of the length of the interval. The results illustrated in this book look into the so-called turnpike property of optimal control problems. The author generalizes the results of the turnpike property by considering a class of optimal control problems which is identified with the corresponding complete metric space of objective functions. This establishes the turnpike property for any element in a set that is in a countable intersection which is open everywhere dense sets in the space of integrands; meaning that the turnpike property holds for most optimal control problems. Mathematicians working in optimal control and the calculus of variations and graduate students will find this book useful and valuable due to its presentation of solutions to a number of difficult problems in optimal control and presentation of new approaches, techniques and methods.
Download or read book Regularization Methods for Ill Posed Optimal Control Problems written by Frank Pörner and published by BoD – Books on Demand. This book was released on 2018-10-04 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ill-posed optimization problems appear in a wide range of mathematical applications, and their numerical solution requires the use of appropriate regularization techniques. In order to understand these techniques, a thorough analysis is inevitable. The main subject of this book are quadratic optimal control problems subject to elliptic linear or semi-linear partial differential equations. Depending on the structure of the differential equation, different regularization techniques are employed, and their analysis leads to novel results such as rate of convergence estimates.
Download or read book Analysis and Finite Element Approximations of Stochastic Optimal Control Problems Constrained by Stochastic Elliptic Partial Differential Equations written by Jangwoon Lee and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book PRACTICAL APPLICATION O OPTIMAL CONTROL THEORY written by QUAN-FANG WANG and published by Lambert Academic Publishing. This book was released on 2011-11-11 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Penalty Methods in Optimal control Theory written by Arnold P. Jones and published by . This book was released on 1969 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent appearance of a paper by A.V. Balakrishnan, in which a penalty function was used to remove the necessity of solving the dynamical equations in order to compute the solution of an optimal control problem, has motivated the developments presented here. Restricting ourselves to a fixed-end-point problem in optimal-control theory with special intermediate and control constraints, we prove that under certain restrictions one may replace this optimal-control problem by a sequence of unconstrained (free) variational problems by the use of a penalty function. This function incorporates the dynamical equations, intermediate-state constraints, and control constraints, as well as the initial-state constraint (initial condition) with appropriate penalties. (Author).
Download or read book Risk Sensitive Optimal Control written by Peter Whittle and published by . This book was released on 1990-05-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two major themes of this book are risk-sensitive control and path-integral or Hamiltonian formulation. It covers risk-sensitive certainty-equivalence principles, the consequent extension of the conventional LQG treatment and the path-integral formulation.
Download or read book Consistent Approximations of Constrained Optimal Control Problems written by Vadim Azhmyakov and published by Logos Verlag Berlin. This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book evolved over a period of years as the author taught classes in numerical analysis, optimization theory and optimal control to graduate students in mathematics and engineering. The material presented in this monograph is the result of author's work at the E.M.A. University of Greifswald and at the Technical University of Berlin. The book has likewise been influenced by my research programs that have relied on the application of the proximal-based numerical schemes and algorithms to constrained optimal control problems. The task of my project was to look closely at the possible consistent techniques of numerical analysis for constrained optimal control problems and the corresponding convergence analysis. The aim of this book is to provide some proximal-type regular computational methods for optimal control processes governed by ordinary differential equations.This book gives a self-contained and systematic exposition of the proximal-regularization methods to optimal control problems with general constraints. It can be used as a textbook for PhD students majoring in mathematical control theory and also serve as a reference for researchers in applied mathematics, control engineering and computational sciences.
Download or read book Stochastic Linear Regulator Problem in Optimal Control Theory written by Md. Azizul Baten and published by LAP Lambert Academic Publishing. This book was released on 2012-03 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic optimization problems are the study of dynamical systems subject to random perturbations which can be controlled in order to optimize some performance criterion. The research on control theory has developed considerably over last few years, inspired in particular by stochastic optimization problems emerging from mathematical nance. Problems involving linear dynamics and quadratic performance criteria are generally called linear regulator problems. The usual framework of control is the one given in probably the most studied control problem, the linear quadratic optimal control problem or the linear regulator problem, which deals with minimizing a performance index of a system governed by a set of dierential equations. The object of linear regulator control problems is to control the position of a certain process and at the same time, the force with which this process is being regulated, by punishing quadratic deviations from some targets of the process and the rate of regulation, respectively.
Download or read book Optimal Control of Stochastic Difference Volterra Equations written by Leonid Shaikhet and published by Springer. This book was released on 2014-12-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equations commences with an historical introduction to the emergence of this type of equation with some additional mathematical preliminaries. It then deals with the necessary conditions for optimality in the control of the equations and constructs a feedback control scheme. The approximation of stochastic quasilinear Volterra equations with quadratic performance functionals is then considered. Optimal stabilization is discussed and the filtering problem formulated. Finally, two methods of solving the optimal control problem for partly observable linear stochastic processes, also with quadratic performance functionals, are developed. Integrating the author’s own research within the context of the current state-of-the-art of research in difference equations, hereditary systems theory and optimal control, this book is addressed to specialists in mathematical optimal control theory and to graduate students in pure and applied mathematics and control engineering.
Download or read book The Theory of Bounded Phase Optimal Control Via the Interior Penalty Method written by David Edmond Cartier and published by . This book was released on 1970 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Application of Penalty Methods to Optimal Control Problems for Functional Differential Equations written by H. Sasai and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Infinite Horizon Optimal Control written by Dean A. Carlson and published by Springer. This book was released on 1991 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Control Theory with Applications in Economics written by Thomas A. Weber and published by MIT Press. This book was released on 2011-09-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.
Download or read book Necessary Conditions for Optimal Control Problems with Bounded State by a Penalty Method written by Negash Gabre Medhin and published by . This book was released on 1900 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
