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.
https://hal.inria.fr/hal-01215556 Contributor : Jean-Luc GouzéConnect in order to contact the contributor Submitted on : Wednesday, October 14, 2015 - 2:44:28 PM Last modification on : Thursday, January 20, 2022 - 5:28:33 PM Long-term archiving on: : Thursday, April 27, 2017 - 4:30:37 AM
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⟩