Lyapunov Functions In Differential Games

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Lyapunov Functions in Differential Games

Author : Vladislav I Zhukovskiy
Publisher : CRC Press
ISBN 13 : 9780415273411
Total Pages : 308 pages
Book Rating : 4.2/5 (734 download)

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Book Synopsis Lyapunov Functions in Differential Games by : Vladislav I Zhukovskiy

Download or read book Lyapunov Functions in Differential Games written by Vladislav I Zhukovskiy and published by CRC Press. This book was released on 2003-01-16 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theory. This approach, which combines dynamic programming and the Lyapunov function method, leads to coefficient criteria, or ratios of the game math model parameters with which optimal strategies of the players not only exist but their analytical form can be specified. In this book coefficient criteria are derived for numerous new and relevant problems in the theory of linear-quadratic multi-player differential games. Those criteria apply when the players formulate their strategies independently (non co-operative games) and use non-Nash equilibria or when the game model recognizes noise, perturbation and other uncertainties of which only their ranges are known (differential games under uncertainty). This text is useful for researchers, engineers and students of applied mathematics, control theory and the engineering sciences.

Lyapunov Functions in Differential Games

Author : Vladislav I Zhukovskiy
Publisher : CRC Press
ISBN 13 : 1482264994
Total Pages : 299 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Lyapunov Functions in Differential Games by : Vladislav I Zhukovskiy

Dynamics, Bifurcations and Control

Author : Fritz Colonius
Publisher : Springer
ISBN 13 : 3540456066
Total Pages : 300 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Dynamics, Bifurcations and Control by : Fritz Colonius

Download or read book Dynamics, Bifurcations and Control written by Fritz Colonius and published by Springer. This book was released on 2003-07-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume originates from the Third Nonlinear Control Workshop "- namics, Bifurcations and Control", held in Kloster Irsee, April 1-3 2001. As the preceding workshops held in Paris (2000) and in Ghent (1999), it was organized within the framework of Nonlinear Control Network funded by the European Union (http://www.supelec.fr/lss/NCN). The papers in this volume center around those control problems where phenomena and methods from dynamical systems theory play a dominant role. Despite the large variety of techniques and methods present in the c- tributions, a rough subdivision can be given into three areas: Bifurcation problems, stabilization and robustness, and global dynamics of control s- tems. A large part of the fascination in nonlinear control stems from the fact that is deeply rooted in engineering and mathematics alike. The contributions to this volume reflect this double nature of nonlinear control. We would like to take this opportunity to thank all the contributors and the referees for their careful work. Furthermore, it is our pleasure to thank Franchise Lamnabhi-Lagarrigue, the coordinator of our network, for her s- port in organizing the workshop and the proceedings and for the tremendous efforts she puts into this network bringing the cooperation between the d- ferent groups to a new level. In particular, the exchange and the active p- ticipation of young scientists, also reflected in the Pedagogical Schools within the Network, is an asset for the field of nonlinear control.

Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems

Author : Cheng-ke Zhang
Publisher : Springer
ISBN 13 : 331940587X
Total Pages : 196 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems by : Cheng-ke Zhang

Download or read book Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems written by Cheng-ke Zhang and published by Springer. This book was released on 2016-09-02 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the achievements of differential game research. This book can be used as a reference book for non-cooperative differential game study, for graduate students majored in economic management, science and engineering of institutions of higher learning.

LQ Dynamic Optimization and Differential Games

Author : Jacob Engwerda
Publisher : John Wiley & Sons
ISBN 13 : 9780470015247
Total Pages : 514 pages
Book Rating : 4.0/5 (152 download)

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Book Synopsis LQ Dynamic Optimization and Differential Games by : Jacob Engwerda

Download or read book LQ Dynamic Optimization and Differential Games written by Jacob Engwerda and published by John Wiley & Sons. This book was released on 2005-06-17 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a wide variety of fields. LQ Dynamic Optimization and Differential Games is an assessment of the state of the art in its field and the first modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management. Linear quadratic dynamic models have a long tradition in economics, operations research and control engineering; and the author begins by describing the one-decision maker LQ dynamic optimization problem before introducing LQ differential games. Covers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback). Includes real-life economic examples to illustrate theoretical concepts and results. Presents problem formulations and sound mathematical problem analysis. Includes exercises and solutions, enabling use for self-study or as a course text. Supported by a website featuring solutions to exercises, further examples and computer code for numerical examples. LQ Dynamic Optimization and Differential Games offers a comprehensive introduction to the theory and practice of this extensively used class of economic models, and will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/graduate students in economics, mathematics, engineering and management science.

The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics

Author : Mindia E. Salukvadze
Publisher : Springer Nature
ISBN 13 : 3030255468
Total Pages : 290 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics by : Mindia E. Salukvadze

Download or read book The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics written by Mindia E. Salukvadze and published by Springer Nature. This book was released on 2020-02-18 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to elaborate on the main principles of the theory of the Berge equilibrium by answering the following two questions: What are the basic properties of the Berge equilibrium? Does the Berge equilibrium exist, and how can it be calculated? The Golden Rule of ethics, which appears in Christianity, Judaism, Islam, Buddhism, Confucianism and other world religions, states the following: “Behave towards others as you would like them to behave towards you." In any game, each party of conflict seeks to maximize some payoff. Therefore, for each player, the Golden Rule is implemented through the maximization of his/her payoff by all other players, which matches well with the concept of the Berge equilibrium. The approach presented here will be of particular interest to researchers (including undergraduates and graduates) and economists focused on decision-making under complex conflict conditions. The peaceful resolution of conflicts is the cornerstone of the approach: as a matter of fact, the Golden Rule precludes military clashes and violence. In turn, the new approach requires new methods; in particular, the existence problems are reduced to saddle point design for the Germeier convolution of payoff functions, with further transition to mixed strategies in accordance with the standard procedure employed by E. Borel, J. von Neumann, J. Nash, and their followers. Moreover, this new approach has proven to be efficient and fruitful with regard to a range of other important problems in mathematical game theory, which are considered in the Appendix.

Differential Games and Applications

Author : Tamer Başar
Publisher :
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Differential Games and Applications by : Tamer Başar

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.

Pursuit-Evasion Differential Games

Author : Y. Yavin
Publisher : Elsevier
ISBN 13 : 1483295931
Total Pages : 352 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Pursuit-Evasion Differential Games by : Y. Yavin

Download or read book Pursuit-Evasion Differential Games written by Y. Yavin and published by Elsevier. This book was released on 2014-06-28 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Twenty papers are devoted to the treatment of a wide spectrum of problems in the theory and applications of dynamic games with the emphasis on pursuit-evasion differential games. The problem of capturability is thoroughly investigated, also the problem of noise-corrupted (state) measurements. Attention is given to aerial combat problems and their attendant modelling issues, such as variable speed of the combatants, the three-dimensionality of physical space, and the combat problem, i.e. problems related to 'role determination'.

Fractional Differential Equations

Author : Anatoly Kochubei
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110571668
Total Pages : 528 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Fractional Differential Equations by : Anatoly Kochubei

Download or read book Fractional Differential Equations written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.

Optimal Adaptive Control and Differential Games by Reinforcement Learning Principles

Author : Draguna L. Vrabie
Publisher : IET
ISBN 13 : 1849194890
Total Pages : 305 pages
Book Rating : 4.8/5 (491 download)

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Book Synopsis Optimal Adaptive Control and Differential Games by Reinforcement Learning Principles by : Draguna L. Vrabie

Download or read book Optimal Adaptive Control and Differential Games by Reinforcement Learning Principles written by Draguna L. Vrabie and published by IET. This book was released on 2013 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews developments in the following fields: optimal adaptive control; online differential games; reinforcement learning principles; and dynamic feedback control systems.

Generalized Solutions of First Order PDEs

Author : Andrei I. Subbotin
Publisher : Springer Science & Business Media
ISBN 13 : 1461208475
Total Pages : 324 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Generalized Solutions of First Order PDEs by : Andrei I. Subbotin

Download or read book Generalized Solutions of First Order PDEs written by Andrei I. Subbotin and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hamilton-Jacobi equations and other types of partial differential equa tions of the first order are dealt with in many branches of mathematics, mechanics, and physics. These equations are usually nonlinear, and func tions vital for the considered problems are not smooth enough to satisfy these equations in the classical sense. An example of such a situation can be provided by the value function of a differential game or an optimal control problem. It is known that at the points of differentiability this function satisfies the corresponding Hamilton-Jacobi-Isaacs-Bellman equation. On the other hand, it is well known that the value function is as a rule not everywhere differentiable and therefore is not a classical global solution. Thus in this case, as in many others where first-order PDE's are used, there arises necessity to introduce a notion of generalized solution and to develop theory and methods for constructing these solutions. In the 50s-70s, problems that involve nonsmooth solutions of first order PDE's were considered by Bakhvalov, Evans, Fleming, Gel'fand, Godunov, Hopf, Kuznetzov, Ladyzhenskaya, Lax, Oleinik, Rozhdestven ski1, Samarskii, Tikhonov, and other mathematicians. Among the inves tigations of this period we should mention the results of S.N. Kruzhkov, which were obtained for Hamilton-Jacobi equation with convex Hamilto nian. A review of the investigations of this period is beyond the limits of the present book. A sufficiently complete bibliography can be found in [58, 126, 128, 141].

Nonlinear and Optimal Control Systems

Author : Thomas L. Vincent
Publisher : John Wiley & Sons
ISBN 13 : 9780471042358
Total Pages : 584 pages
Book Rating : 4.0/5 (423 download)

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Book Synopsis Nonlinear and Optimal Control Systems by : Thomas L. Vincent

Download or read book Nonlinear and Optimal Control Systems written by Thomas L. Vincent and published by John Wiley & Sons. This book was released on 1997-06-23 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback control systems. There is special emphasis on the fundamental topics of stability, controllability, and optimality, and on the corresponding geometry associated with these topics. Each chapter contains several examples and a variety of exercises.

Control and Dynamic Systems V35: Advances in Control Mechanics Part 2 of 2

Author : C.T. Leonides
Publisher : Academic Press
ISBN 13 : 0323162568
Total Pages : 335 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Control and Dynamic Systems V35: Advances in Control Mechanics Part 2 of 2 by : C.T. Leonides

Download or read book Control and Dynamic Systems V35: Advances in Control Mechanics Part 2 of 2 written by C.T. Leonides and published by Academic Press. This book was released on 2012-12-02 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Control Mechanics is based on a National Science Foundation-Sponsored Workshop on Control Mechanics, i.e., control system development using analytical methods of mechanics and active control of mechanical systems. Publication of the presentations at this workshop in this Academic Press series has made it possible to expand them into a format which will facilitate the study and utilization of their significant results by working professionals and research workers on the international scene. This book comprises 13 chapters, with the first focusing on recursive Lyapunov functions, particularly their properties and linear systems. Succeeding chapters tackle topics such as the Lyapunov functional approach to uncertain systems governed by functional differential equations with finite time-lag; and stabilizing discrete control laws for Hamiltonian systems. Other chapters cover component model reduction in canonical correlation coordinates; controlling a flexible plate to mimic a rigid one; the modal stability of imperfect cyclic systems; and simultaneous stabilization via low order controllers. The remaining chapters discuss the use of Liapunov techniques for collision-avoidance of robot arms; avoidance control of a two-point mechanical system; coordination controllers for multi-arm manipulators; MRAC techniques with application to robot manipulators; optimal preview controllers based upon explicit trajectory models; and analysis of a robot dragline for mining. This book will be of interest to practitioners in the fields of engineering and aeronautics.

Hybrid Systems: Computation and Control

Author : Oded Maler
Publisher : Springer Science & Business Media
ISBN 13 : 3540009132
Total Pages : 569 pages
Book Rating : 4.5/5 (4 download)

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Book Synopsis Hybrid Systems: Computation and Control by : Oded Maler

Download or read book Hybrid Systems: Computation and Control written by Oded Maler and published by Springer Science & Business Media. This book was released on 2003-03-18 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitues the refereed proceedings of the 6th International Workshop on Hybrid Systems: Computation and Control, HSCC 2003, held in Prague, Czech Republic, in April 2003. The 36 revised full papers presented were carefully reviewed and selected from 75 submissions. All current issues in hybrid systems are addressed including formal methods for analysis and control, computational tools, as well as innovative applications in various fields such as automotive control, the immune system, electrical circuits, operating systems, and human brains.

Hybrid Systems: Computation and Control

Author : Freek Wiedijk
Publisher : Springer
ISBN 13 : 354036580X
Total Pages : 569 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Hybrid Systems: Computation and Control by : Freek Wiedijk

Download or read book Hybrid Systems: Computation and Control written by Freek Wiedijk and published by Springer. This book was released on 2003-07-01 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Sixth Workshop on Hybrid Systems: Computation and Control (HSCC 2003), which was held in Prague, during April 3–5, 2003. The Hybrid Systems workshops attract researchers interested in the modeling, analysis, control, and implementation of systems which involve the interaction of both discrete and continuous state dynamics. The newest results and latest developments in hybrid system models, formal methods for analysis and control, computational tools, as well as new applications and examples are presented at these annual meetings. The Sixth Workshop continued the series of workshops held in Grenoble, France (HART’97), Berkeley, California, USA (HSCC’98), Nijmegen, The Neth- lands (HSCC’99), Pittsburgh, Pennsylvania, USA (HSCC 2000), Rome, Italy (HSCC 2001), and Stanford, California, USA (HSCC 2002). Proceedings of these workshops have been published by Springer-Verlag in the Lecture Notes in C- puter Science (LNCS) series. This year we assembled a technical program committee with a broad expertise in formal methods in computer science, control theory, applied mathematics, and arti?cial intelligence. We received a set of 75 high-quality submitted papers. After detailed review and discussion of these papers by the program committee, 36 papers were accepted for presentation at the workshop, and the ?nal versions of these papers appear in this volume.

Set-Theoretic Methods in Control

Author : Franco Blanchini
Publisher : Birkhäuser
ISBN 13 : 3319179330
Total Pages : 640 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Set-Theoretic Methods in Control by : Franco Blanchini

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

Asymptotic Behavior of Dynamical and Control Systems under Pertubation and Discretization

Author : Lars Grüne
Publisher : Springer
ISBN 13 : 3540367845
Total Pages : 241 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Asymptotic Behavior of Dynamical and Control Systems under Pertubation and Discretization by : Lars Grüne

Download or read book Asymptotic Behavior of Dynamical and Control Systems under Pertubation and Discretization written by Lars Grüne and published by Springer. This book was released on 2004-10-19 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors, asumptotically controllable sets and their respective domains of attractions and reachable sets. Combining robust stability concepts from nonlinear control theory, techniques from optimal control and differential games and methods from nonsmooth analysis, both qualitative and quantitative results are obtained and new algorithms are developed, analyzed and illustrated by examples.