Lyapunov functions in differential games /
Vladislav I. Zhukovskiy.
London ; New York : Taylor & Francis, 2002.
xvi, 281 p. : ill.
0415273412 (hb)
More Details
London ; New York : Taylor & Francis, 2002.
0415273412 (hb)
catalogue key
Includes bibliographical references and index.
A Look Inside
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SciTech Book News, September 2003
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Back Cover Copy
This book explores the solution of dynamical games problems under uncertainty by means of the Bellman-Lyapunov function. In Part One the author describes the foundations of differential games under uncertainties and presents examples from economic dynamics needed for the investigation. He focuses on the notion of the vector guarantee, its properties, and the methods of construction. Part Two explores differential linear quadratic games under uncertainty. Here the author proposes new guaranteeing solutions based on the concept of the equilibrium of objections and counter-objections as well as the active equilibrium. Each chapter includes exercises, and solutions are provided at the end of the book.
Main 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.
Table of Contents
The Simplist Concepts and Examples
Some Concepts in the Theory of Differential Games Under Uncertainty
Game Problems in Mechanical and Economical Systems
Vector-Valued Guarantees
Vector-Valued Guarantees Can Exist or Not
Converse Problem
Equilibrium of Nash Under Uncertainty
Equilibrium of Threats and Counterthreats Under Uncertainty
Singularities of the Nash Equilibrium
Formalization and Properties Unimprovable Equilibriums
Comparison with Nash Equilibrium
Formalization of
Table of Contents provided by Publisher. All Rights Reserved.

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