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Pursuit-Evasion Games and Zero-sum Two-person Differential Games

Pierre Bernhard 1
1 BIOCORE - Biological control of artificial ecosystems
INRA - Institut National de la Recherche Agronomique, CRISAM - Inria Sophia Antipolis - Méditerranée , LOV - Laboratoire d'océanographie de Villefranche
Abstract : Differential games arose from the investigation, by Rufus Isaacs in the 50's, 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.
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Pierre Bernhard. Pursuit-Evasion Games and Zero-sum Two-person Differential Games. Encyclopaedia of Systems and Control, Springer-Verlag, pp.8, 2015, ⟨10.1007/978-1-4471-5102-9_270-1⟩. ⟨hal-01215556⟩

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