Stochastic and Differential Games: Theory and Numerical Methods: 4 (Annals of the International Society of Dynamic Games) - Softcover

Softcover

ISBN 10: 1461272084 ISBN 13: 9781461272083

Verlag: Birkhäuser, 2012

Inhaltsangabe

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.

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Reseña del editor

This volume presents state-of-the-art surveys, new results, and algorithms that will interest applied mathematicians, control engineers, and operations research specialists. It covers such diverse topics as pursuit-evasion games, viscosity solutions, gambling theory, discounted stochastic games, optimal routing, numerical methods, and others. The volume consists of two parts, with the first dealing with zero-sum differential games and numerical methods, and the second with stochastic and nonzero-sum games, and applications.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 1461272084
• ISBN 13: 9781461272083
• Einband: Tapa blanda
• Anzahl der Seiten: 400
• Herausgeber: Bardi Martino, Raghavan T.E.S., Parthasarathy T.
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar