Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Pursuit-Evasion Games and Zero-Sum Two-Person Differential Games

  • Pierre Bernhard
Reference work entry
First Online:
DOI: https://doi.org/10.1007/978-1-4471-5058-9_270
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Abstract

Differential games arose from the investigation, by Rufus Isaacs in the 1950s, of pursuit-evasion problems. In these problems, closed-loop strategies are of the essence, although defining what is exactly meant by this phrase, and what is the “Value” of a differential game, is difficult. For closed-loop strategies, there is no such thing as a “two-sided maximum principle,” and one must resort to the analysis of Isaacs’ equation, a Hamilton Jacobi equation. The concept of viscosity solutions of Hamilton-Jacobi equations has helped solve several of these issues.

Keywords

Closed loop strategies Isaacs’ condition Viscosity solutions 
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© Springer-Verlag London 2015

Authors and Affiliations

  • Pierre Bernhard
    • 1
  1. 1.INRIA-Sophia Antipolis MéditerranéeSophia AntipolisFrance