Overview

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.

Full Product Details

Author:   Martino Bardi ,  T.E.S. Raghavan ,  T. Parthasarathy
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1999
Volume:   4
Dimensions:   Width: 15.50cm , Height: 2.10cm , Length: 23.50cm
Weight:   0.611kg
ISBN:  

9781461272083

ISBN 10:   1461272084
Pages:   381
Publication Date:   24 December 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

I. Zero-Sum Differential Games and Numerical Methods.- 1 Constructive Theory of Positional Differential Games and Generalized Solutions to Hamilton—Jacobi Equations.- 2 Two-Player, Zero-Sum Differential Games and Viscosity Solutions.- 3 Numerical Methods for Pursuit-Evasion Games via Viscosity Solutions.- 4 Set-Valued Numerical Analysis for Optimal Control and Differential Games.- II. Stochastic and Nonzero-Sum Games and Applications.- 5 An Introduction to Gambling Theory and Its Applications to Stochastic Games.- 6 Discounted Stochastic Games: A Complex Analytic Perspective.- 7 Nonzero-Sum Stochastic Games.- 8 The Power of Threats in Stochastic Games.- 9 A Markov Game Approach for Optimal Routing Into a Queuing Network.- 10 On Linear Complementarity and A Discounted Polystochastic Game.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions