PURSUIT-EVASION PROBLEMS AND VISCOSITY SOLUTIONS OF ISAACS EQUATIONS

Authors
Citation
P. Soravia, PURSUIT-EVASION PROBLEMS AND VISCOSITY SOLUTIONS OF ISAACS EQUATIONS, SIAM journal on control and optimization, 31(3), 1993, pp. 604-623
Citations number
42
Categorie Soggetti
Controlo Theory & Cybernetics",Mathematics
ISSN journal
03630129
Volume
31
Issue
3
Year of publication
1993
Pages
604 - 623
Database
ISI
SICI code
0363-0129(1993)31:3<604:PPAVSO>2.0.ZU;2-N
Abstract
The Dirichlet problem for first-order Hamilton-Jacobi equations arisin g in differential games of pursuit and evasion is studied. Local and g lobal sub- and superoptimality principles are stated for, respectively , viscosity sub- and supersolutions. These results are applied to obta in 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 approa ch used in this paper allows Lyapunov functions satisfying the usual c ondition in the weak sense of viscosity solutions.