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Author: Pan-Tai Liu
Publisher: CRC Press
ISBN: 1000153428
Category : Mathematics
Languages : en
Pages : 262
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Book Description
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: Pan-Tai Liu
Publisher: CRC Press
ISBN: 1000153428
Category : Mathematics
Languages : en
Pages : 262
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Book Description
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: Avner Friedman
Publisher: Courier Corporation
ISBN: 0486153274
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Graduate-level text surveys games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, games with restricted phase coordinates, and N-person games. 1971 edition.
Author: Alexander Tarasyev
Publisher: Springer Nature
ISBN: 3030428311
Category : Technology & Engineering
Languages : en
Pages : 380
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Book Description
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: Engelbert Dockner
Publisher: Cambridge University Press
ISBN: 9780521637329
Category : Business & Economics
Languages : en
Pages : 398
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Book Description
A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics.
Author: Rufus Isaacs
Publisher: Courier Corporation
ISBN: 0486135985
Category : Mathematics
Languages : en
Pages : 420
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Book Description
Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.
Author: Vladislav I Zhukovskiy
Publisher: CRC Press
ISBN: 9780415273411
Category : Mathematics
Languages : en
Pages : 308
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Book Description
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: Rene Carmona
Publisher: SIAM
ISBN: 1611974240
Category : Mathematics
Languages : en
Pages : 263
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Book Description
The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.
Author: Tamer S. Basar
Publisher: Springer
ISBN: 9783662168660
Category : Technology & Engineering
Languages : en
Pages : 205
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Book Description
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.
Author: Suresh P. Sethi
Publisher: Taylor & Francis US
ISBN: 9780387280929
Category : Business & Economics
Languages : en
Pages : 536
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Book Description
Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the authors have applied to business management problems developed from their research and classroom instruction. Sethi and Thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on Optimal Control Theory. The new edition has been completely refined with careful attention to the text and graphic material presentation. Chapters cover a range of topics including finance, production and inventory problems, marketing problems, machine maintenance and replacement, problems of optimal consumption of natural resources, and applications of control theory to economics. The book contains new results that were not available when the first edition was published, as well as an expansion of the material on stochastic optimal control theory.
Author: Alain Bensoussan
Publisher: Springer Science & Business Media
ISBN: 1461485088
Category : Science
Languages : en
Pages : 132
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Book Description
Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem.
