Pursuit–Evasion Problems and Viscosity Solutions of Isaacs Equations

Author:
Publisher website
Google Scholar
Abstract
The Dirichlet problem for first-order Hamilton–Jacobi equations arising in differential games of pursuit and evasion is studied. Local and global sub- and superoptimality principles are stated for, respectively, viscosity sub- and supersolutions. These results are applied to obtain a general existence theorem and to prove the existence of the value of the game. The main application concerns the problem of stability (terminability) of a dynamical system with two competitive controls and the opposite one of evadability from a general closed set. The approach used in this paper allows Lyapunov functions satisfying the usual condition in the weak sense of viscosity solutions.

This publication has 25 references indexed in Scilit: