| Lyapunov Functions in Differential Games Contributor(s): Zhukovskiy, Vladislav I. (Author) |
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ISBN: 0415273412 ISBN-13: 9780415273411 Publisher: CRC Press OUR PRICE: $256.50 Product Type: Hardcover - Other Formats Published: January 2003 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Game Theory - Mathematics | Differential Equations - General - Mathematics | Applied |
| Dewey: 519.3 |
| LCCN: 2002035979 |
| Series: Stability and Control: Theory, Methods and Applications |
| Physical Information: 0.85" H x 7.04" W x 9.88" (1.50 lbs) 304 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |
