Stability Control And Differential Games

Author : Alexander Tarasyev,Vyacheslav Maksimov,Tatiana Filippova
Publisher : Springer Nature
Page : 380 pages
File Size : 50,5 Mb
Release : 2020-05-29
Category : Technology & Engineering
ISBN : 9783030428310

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Stability, Control and Differential Games by Alexander Tarasyev,Vyacheslav Maksimov,Tatiana Filippova Pdf

This book presents the proceedings of the International Conference “Stability, Control, Differential Games” (SCDG2019, September 16 – 20, 2019, Yekaterinburg, Russia), organized by the Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences. Discussing the latest advances in the theory of optimal control, stability theory and differential games, it also demonstrates the application of new techniques and numerical algorithms to solve problems in robotics, mechatronics, power and energy systems, economics and ecology. Further, the book includes fundamental results in control theory, stability theory and differential games presented at the conference, as well as a number of chapters focusing on novel approaches in solving important applied problems in control and optimization. Lastly, it evaluates recent major accomplishments, and forecasts developments in various up-and-coming areas, such as hybrid systems, model predictive control, Hamilton–Jacobi equations and advanced estimation algorithms.

Author : David W. K. Yeung,Leon A. Petrosyan
Publisher : Springer Nature
Page : 311 pages
File Size : 41,5 Mb
Release : 2022-03-31
Category : Mathematics
ISBN : 9783030927424

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Durable-Strategies Dynamic Games by David W. K. Yeung,Leon A. Petrosyan Pdf

Durable strategies that have prolonged effects are prevalent in real-world situations. Revenue-generating investments, toxic waste disposal, long-lived goods, regulatory measures, coalition agreements, diffusion of knowledge, advertisement and investments to accumulate physical capital are concrete and common examples of durable strategies. This book provides an augmentation of dynamic game theory and advances a new game paradigm with durable strategies in decision-making schemes. It covers theories, solution techniques, and the applications of a general class of dynamic games with multiple durable strategies. Non-cooperative equilibria and cooperative solutions are derived, along with advanced topics including random termination, asynchronous game horizons, and stochastic analysis. The techniques presented here will enable readers to solve numerous practical dynamic interactive problems with durable strategies. This book not only expands the scope of applied dynamic game theory, but also provides a solid foundation for further theoretical and technical advancements. As such, it will appeal to scholars and students of quantitative economics, game theory, operations research, and computational mathematics. "Not too many new concepts have been introduced in dynamic games since their inception. The introduction of the concept of durable strategies changes this trend and yields important contributions to environmental and business applications." Dušan M Stipanović, Professor, University of Illinois at Urbana-Champaign "Before this book, the field simply did not realize that most of our strategies are durable and entail profound effects in the future. Putting them into the mathematical framework of dynamic games is a great innovative effort." Vladimir Turetsky, Professor, Ort Braude College “Durable-strategies Dynamic Games is truly a world-leading addition to the field of dynamic games. It is a much needed publication to tackle increasingly crucial problems under the reality of durable strategies.” Vladimir Mazalov, Director of Mathematical Research, Russian Academy of Sciences & President of the International Society of Dynamic Games

Author : Vladislav I Zhukovskiy
Publisher : CRC Press
Page : 308 pages
File Size : 52,6 Mb
Release : 2003-01-16
Category : Mathematics
ISBN : 0415273412

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Lyapunov Functions in Differential Games by Vladislav I Zhukovskiy Pdf

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.

Author : Panos Pardalos,Michael Khachay,Vladimir Mazalov
Publisher : Springer Nature
Page : 332 pages
File Size : 51,8 Mb
Release : 2022-06-24
Category : Mathematics
ISBN : 9783031096075

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Mathematical Optimization Theory and Operations Research by Panos Pardalos,Michael Khachay,Vladimir Mazalov Pdf

This book constitutes the proceedings of the 21st International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2022, held in Petrozavodsk, Russia, in July 2022. The 21 full papers presented together with 6 invited abstracts lectures and 2 tutorial abstracts in this volume were carefully reviewed and selected from 88 submissions. The conference focuses on the following topics: Mathematical programming, bi-level and global optimization, integer programming and combinatorial optimization, approximation algorithms with theoretical guarantees and approximation schemes, heuristics and meta-heuristics, game theory, optimal control, optimization in machine learning and data analysis, and their valuable applications in operations research and economics.

Author : Vladislav I Zhukovskiy
Publisher : CRC Press
Page : 304 pages
File Size : 55,6 Mb
Release : 2003-01-16
Category : Mathematics
ISBN : 9781482264999

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Lyapunov Functions in Differential Games by Vladislav I Zhukovskiy Pdf

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 theor

Author : Luca Lambertini
Publisher : Unknown
Page : 275 pages
File Size : 49,7 Mb
Release : 2018-04-26
Category : Business & Economics
ISBN : 9781107164680

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Differential Games in Industrial Economics by Luca Lambertini Pdf

A comprehensive and self-contained exposition of the applications of optimal control and differential game theory to industrial organisation and trade.

Author : Lev Semenovich Pontri︠a︡gin
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 48,7 Mb
Release : 1990
Category : Mathematics
ISBN : 0821831348

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Optimal Control and Differential Games by Lev Semenovich Pontri︠a︡gin Pdf

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."

Author : V. N. Lagunov
Publisher : Unknown
Page : 304 pages
File Size : 47,9 Mb
Release : 1985
Category : Control theory
ISBN : UOM:39015015627063

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Introduction to Differential Games and Control Theory by V. N. Lagunov Pdf

Author : Pan-Tai Liu
Publisher : CRC Press
Page : 262 pages
File Size : 52,8 Mb
Release : 2020-12-18
Category : Mathematics
ISBN : 9781000153422

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Differential Games and Control Theory Iii by Pan-Tai Liu Pdf

This book is based on the Third Kingston Conference on Differential Games and Control Theory held at the University of Rhode Island June 5-8, 1978. It deals with deterministic systems and stochastic systems, and is helpful for the researchers in applied mathematics.

Author : Bor-Sen Chen
Publisher : CRC Press
Page : 600 pages
File Size : 42,9 Mb
Release : 2019-07-31
Category : Mathematics
ISBN : 9780429780516

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Stochastic Game Strategies and their Applications by Bor-Sen Chen Pdf

Game theory involves multi-person decision making and differential dynamic game theory has been widely applied to n-person decision making problems, which are stimulated by a vast number of applications. This book addresses the gap to discuss general stochastic n-person noncooperative and cooperative game theory with wide applications to control systems, signal processing systems, communication systems, managements, financial systems, and biological systems. H∞ game strategy, n-person cooperative and noncooperative game strategy are discussed for linear and nonlinear stochastic systems along with some computational algorithms developed to efficiently solve these game strategies.

Author : Martino Bardi,T.E.S. Raghavan,T. Parthasarathy
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215929

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Stochastic and Differential Games by Martino Bardi,T.E.S. Raghavan,T. Parthasarathy Pdf

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.

Author : Valery Y. Glizer,Oleg Kelis
Publisher : Springer Nature
Page : 211 pages
File Size : 44,9 Mb
Release : 2022-08-29
Category : Mathematics
ISBN : 9783031070518

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Singular Linear-Quadratic Zero-Sum Differential Games and H∞ Control Problems by Valery Y. Glizer,Oleg Kelis Pdf

This monograph is devoted to the analysis and solution of singular differential games and singular $H_{\inf}$ control problems in both finite- and infinite-horizon settings. Expanding on the authors’ previous work in this area, this novel text is the first to study the aforementioned singular problems using the regularization approach. After a brief introduction, solvability conditions are presented for the regular differential games and $H_{\inf}$ control problems. In the following chapter, the authors solve the singular finite-horizon linear-quadratic differential game using the regularization method. Next, they apply this method to the solution of an infinite-horizon type. The last two chapters are dedicated to the solution of singular finite-horizon and infinite-horizon linear-quadratic $H_{\inf}$ control problems. The authors use theoretical and real-world examples to illustrate the results and their applicability throughout the text, and have carefully organized the content to be as self-contained as possible, making it possible to study each chapter independently or in succession. Each chapter includes its own introduction, list of notations, a brief literature review on the topic, and a corresponding bibliography. For easier readability, detailed proofs are presented in separate subsections. Singular Linear-Quadratic Zero-Sum Differential Games and $H_{\inf}$ Control Problems will be of interest to researchers and engineers working in the areas of applied mathematics, dynamic games, control engineering, mechanical and aerospace engineering, electrical engineering, and biology. This book can also serve as a useful reference for graduate students in these area

Author : Jacob Engwerda
Publisher : John Wiley & Sons
Page : 514 pages
File Size : 43,6 Mb
Release : 2005-06-17
Category : Business & Economics
ISBN : 0470015241

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LQ Dynamic Optimization and Differential Games by Jacob Engwerda Pdf

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.

Author : Yuriy P. Kondratenko,Arkadii A. Chikrii,Vyacheslav F. Gubarev,Janusz Kacprzyk
Publisher : Springer
Page : 337 pages
File Size : 54,7 Mb
Release : 2019-05-24
Category : Technology & Engineering
ISBN : 9783030219277

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Advanced Control Techniques in Complex Engineering Systems: Theory and Applications by Yuriy P. Kondratenko,Arkadii A. Chikrii,Vyacheslav F. Gubarev,Janusz Kacprzyk Pdf

This book presents an authoritative collection of contributions by researchers from 16 different countries (Austria, Chile, Georgia, Germany, Mexico, Norway, P.R. of China, Poland, North Macedonia, Romania, Russia, Spain, Turkey, Ukraine, the United Kingdom and United States) that report on recent developments and new directions in advanced control systems, together with new theoretical findings, industrial applications and case studies on complex engineering systems. This book is dedicated to Professor Vsevolod Mykhailovych Kuntsevich, an Academician of the National Academy of Sciences of Ukraine, and President of the National Committee of the Ukrainian Association on Automatic Control, in recognition of his pioneering works, his great scientific and scholarly achievements, and his years of service to many scientific and professional communities, notably those involved in automation, cybernetics, control, management and, more specifically, the fundamentals and applications of tools and techniques for dealing with uncertain information, robustness, non-linearity, extremal systems, discrete control systems, adaptive control systems and others. Covering essential theories, methods and new challenges in control systems design, the book is not only a timely reference guide but also a source of new ideas and inspirations for graduate students and researchers alike. Its 15 chapters are grouped into four sections: (a) fundamental theoretical issues in complex engineering systems, (b) artificial intelligence and soft computing for control and decision-making systems, (c) advanced control techniques for industrial and collaborative automation, and (d) modern applications for management and information processing in complex systems. All chapters are intended to provide an easy-to-follow introduction to the topics addressed, including the most relevant references. At the same time, they reflect various aspects of the latest research work being conducted around the world and, therefore, provide information on the state of the art.

Author : Thomas L. Vincent,Walter J. Grantham
Publisher : John Wiley & Sons
Page : 584 pages
File Size : 49,9 Mb
Release : 1997-06-23
Category : Science
ISBN : 0471042358

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Nonlinear and Optimal Control Systems by Thomas L. Vincent,Walter J. Grantham Pdf

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.