Download or read book Hamilton Jacobi Approach for State Constrained Differential Games and Numerical Learning Methods for Optimal Control Problems written by Nidhal Gammoudi and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis will focus on the study of a theoretical and numerical approach for the multi-objective control problems with state constraints. Multi-objective optimization is an important approach for modelling complex problems in order to analyse the balance between different criteria to minimize. Here, the approach that will be used is based on the theory of Hamilton-Jacobi equations. The goal is to introduce a new methodology to study the properties and compute the Pareto front for multi-objective problems using the value function of an optimal control problem.
Download or read book Stochastic and Differential Games written by Martino Bardi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L.S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P.P. Varaiya, E. Roxin, R.J. Elliott and N.J. Kalton, N.N. Krasovskii, and A.I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L.D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M.G. Crandall and P.-L.
Download or read book Numerical Methods for Optimal Control Problems with State Constraints written by Radoslaw Pytlak and published by Springer. This book was released on 2006-11-14 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.
Download or read book Advances in Dynamic Games written by Michèle Breton and published by Springer Science & Business Media. This book was released on 2010-11-18 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications. The selected contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 13th International Symposium of Dynamic Games and Applications held in Wrocław. The book covers a variety of topics, ranging from theoretical developments in game theory and algorithmic methods to applications, examples, and analysis in fields as varied as environmental management, finance and economics, engineering, guidance and control, and social interaction.
Download or read book Numerical Methods for Optimal Control Problems written by Maurizio Falcone and published by Springer. This book was released on 2019-01-26 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.
Download or read book Optimal Control and Viscosity Solutions of Hamilton Jacobi Bellman Equations written by Martino Bardi and published by Birkhauser. This book was released on 1997 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamiltona "Jacobi type and its interplay with Bellmana (TM)s dynamic programming approach to optimal control and differential games, as it developed after the beginning of the 1980s with the pioneering work of M. Crandall and P.L. Lions. The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about a mathematical theory providing a correct framework for the classical method of dynamic programming as well as mathematicians interested in new methods for first-order nonlinear PDEs. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book. "The exposition is self-contained, clearly written and mathematically precise. The exercises and open problemsa ]will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area." a " Mathematical Reviews "With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercisesa ]Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." a " ZAA "The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field. However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my opinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." a " Zentralblatt MATH "The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)...In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." a " Acta Applicandae Mathematicae
Download or read book Proceedings of 2023 7th Chinese Conference on Swarm Intelligence and Cooperative Control written by Yongzhao Hua and published by Springer Nature. This book was released on with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Index written by A. V. Balakrishnan M. Thoma and published by Springer. This book was released on 2013-11-21 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient Algorithms for Solving Hamilton Jacobi Bellman Equations written by Hamood Amur Hamood Alwardi and published by . This book was released on 2010 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis addresses the construction of some algorithms for numerically solving optimal feedback control problems. Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. More precisely, optimal control problems involve a dynamic system with input quantities, called controls, and some quantity, called cost, to be minimized. An optimal control is a set of differential equations describing the paths of the control variables that optimise the cost. Finding solutions to problems of this nature involves a significantly high degree of difficulty in terms of cost and power compared with the related task of solving optimal open-loop control problems. Moreover, stability is a major problem in the feedback control problem, which may tend to overcorrect errors that can cause oscillations of constant or changing amplitude. A feedback control problem essentially depends on both state and time variables, and so its determination by numerical schemes has one serious drawback, it is the so called curse of dimensionality. Therefore, efficient numerical methods are needed for the accurate determination of optimal feedback controls. There are essentially two equivalent ways in widespread use today to solve optimal feedback control problems. In the first approach, often referred to as the direct approach, the optimal feedback control problem is approximated by considering the optimisation of an objective functional with respect to the control function. This optimisation is subject to the system dynamics and numerous constraints on the state and control variables. In the second approach, the optimal feedback control problem is transformed into a first order terminal value problem by formulating the problem as a nonlinear hyperbolic partial differential equation, known as the Hamilton-Jacobi-Bellman (HJB) equation. In this thesis we consider some numerical algorithms for solving the HJB equation, based on Radial Basis Functions (RBFs). We present a new adaptive least-squares collocation RBFs method for solving a HJB equation. The method involves the use of the least squares method using a set of RBFs in space variables, combined with the implicit backward Euler finite difference method in time, to create an unconditionally stable solution scheme. We also present some of the more theoretical aspects related to the solution of the HJB equation using the adaptive least-squares collocation RBFs method, especially, the relevant existence, uniqueness and stability results. We demonstrate the accuracy and effectiveness of this method by performing numerical experiments on test problems with up to three states and two control variables. Furthermore, we construct another numerical method based on a domain decomposition method using a matrix inversion technique for solving HJB equation. In this method, we propose a new formula for inverting nonsymmetric and full dense coefficient matrix faster than the classical matrix inversion techniques. We also investigate the accuracy of the numerical solution, condition numbers of the system matrix, and the computational time when increasing the number of subdomains. We perform some numerical experiments to illustrate the usefulness and accuracy of the method.
Download or read book Hamilton Jacobi Equations Approximations Numerical Analysis and Applications written by Yves Achdou and published by Springer. This book was released on 2013-05-24 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).
Download or read book Set Theoretic Methods in Control written by Franco Blanchini and published by Birkhäuser. This book was released on 2015-07-02 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this monograph describes the set-theoretic approach for the control and analysis of dynamic systems, both from a theoretical and practical standpoint. This approach is linked to fundamental control problems, such as Lyapunov stability analysis and stabilization, optimal control, control under constraints, persistent disturbance rejection, and uncertain systems analysis and synthesis. Completely self-contained, this book provides a solid foundation of mathematical techniques and applications, extensive references to the relevant literature, and numerous avenues for further theoretical study. All the material from the first edition has been updated to reflect the most recent developments in the field, and a new chapter on switching systems has been added. Each chapter contains examples, case studies, and exercises to allow for a better understanding of theoretical concepts by practical application. The mathematical language is kept to the minimum level necessary for the adequate formulation and statement of the main concepts, yet allowing for a detailed exposition of the numerical algorithms for the solution of the proposed problems. Set-Theoretic Methods in Control will appeal to both researchers and practitioners in control engineering and applied mathematics. It is also well-suited as a textbook for graduate students in these areas. Praise for the First Edition "This is an excellent book, full of new ideas and collecting a lot of diverse material related to set-theoretic methods. It can be recommended to a wide control community audience." - B. T. Polyak, Mathematical Reviews "This book is an outstanding monograph of a recent research trend in control. It reflects the vast experience of the authors as well as their noticeable contributions to the development of this field...[It] is highly recommended to PhD students and researchers working in control engineering or applied mathematics. The material can also be used for graduate courses in these areas." - Octavian Pastravanu, Zentralblatt MATH
Download or read book Differential Games written by Raimo P. Hämäläinen and published by Springer. This book was released on 1991 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Control and Differential Games written by Georges Zaccour and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control and differential games continue to attract strong interest from researchers interested in dynamical problems and models in management science. This volume explores the application of these methodologies to new as well as to classical decision problems in management sciences and economics. In Part I, optimal control and dynamical systems approaches are used to analyze problems in areas such as monetary policy, pollution control, relationship marketing, drug control, debt financing, and ethical behavior. In Part II differential games are applied to problems such as oligopolistic competition, common resource management, spillovers in foreign direct investments, marketing channels, incentive strategies, and the computation of Markov perfect Nash equilibria. Optimal Control and Differential Games is an excellent reference for researchers and graduate students covering a wide range of emerging and revisited problems in management science.
Download or read book Differential Games and Applications written by Tamer Başar and published by . This book was released on 1989 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains fifteen articles on the topic of differential and dynamic games, focusing on both theory and applications. It covers a variety of areas and presents recent developments on topics of current interest. It should be useful to researchers in differential and dynamic games, systems and control, operations research and mathematical economics.
Download or read book Introduction to Differential Games and Control Theory written by V. N. Lagunov and published by . This book was released on 1985 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Control and Differential Games written by Lev Semenovich Pontri︠a︡gin and published by American Mathematical Soc.. This book was released on 1990 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of 22 papers devoted to questions of optimal control theory and differential games, providing an overview of current trends of research in the area of control systems. Numerous optimization methods are covered as well as necessary and sufficient conditions for optimality."
Download or read book Advances in Dynamic Games written by Pierre Cardaliaguet and published by Springer Science & Business Media. This book was released on 2012-09-10 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications. Its contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 14th International Symposium of Dynamic Games and Applications held in Banff. Advances in Dynamic Games covers a variety of topics, ranging from evolutionary games, theoretical developments in game theory and algorithmic methods to applications, examples, and analysis in fields as varied as mathematical biology, environmental management, finance and economics, engineering, guidance and control, and social interaction. Featured throughout are valuable tools and resources for researchers, practitioners, and graduate students interested in dynamic games and their applications to mathematics, engineering, economics, and management science.
