Lyapunov Functions in Differential Games (Stability and Control: Theory, Methods and Applications) - Hardcover

Zhukovskiy, Vladislav I

Hardcover

ISBN 10: 0415273412 ISBN 13: 9780415273411

Publisher: CRC Press, 2003

Synopsis

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.

About this title

About the Author

Vladislav I Zhukovskiy

Edition details

• Publisher: CRC Press
• Publication date: 2003
• Language: English
• ISBN 10: 0415273412
• ISBN 13: 9780415273411
• Binding: Hardcover
• Edition number: 1
• Number of pages: 304