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

International audienceDifferential 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