Nonsmooth semipermeable barriers, Isaacs’ equation, and application to a differential game with one target and two players

Nonsmooth semipermeable barriers, Isaacs’ equation, and application to a differential game with... We study the target problem which is a differential game where one of the players aims at reaching a target while the other player aims at avoiding this target forever. We characterize the victory domains of the players by means of geometric conditions and prove that the boundary of the victory domains is a nonsmooth semipermeable surface, i.e., is a solution (in a weak sense) of the Isaacs equation: sup u inf v ⟨ f ( x, u, v ), p ⟩ = 0, where f is the dynamic of the system, u and v are the respective controls of the players, and p is a normal to the boundary of the victory domains at the point x . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Nonsmooth semipermeable barriers, Isaacs’ equation, and application to a differential game with one target and two players

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Publisher
Springer-Verlag
Copyright
Copyright © 1997 by Springer-Verlag New York Inc.
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/BF02683340
Publisher site
See Article on Publisher Site

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