Nonsmooth analysis and sufficient conditions for a saddle in a differential game (Q1095056)

The paper presents sufficient conditions for a saddle point in a two- player zero-sum constrained differential game, subject to a differential inclusion. Necessary conditions were recently given by the authors [``Nonsmooth analysis and differential games'', in: Operator methods for optimal control, M. Dekker, New York (1987)]. Using nonsmooth analysis [see \textit{F. H. Clarke} ``Optimization and nonsmooth analysis'' (1983; Zbl 0582.49001)] the Isaacs-Bellman equations are obtained for the case where the value function satisfies a Lipschitz condition. Another approach to the Isaacs-Bellman equation is by using viscosity solutions [see \textit{A. I. Subbotin} and \textit{A. M. Taras'ev}, Probl. Control Inf. Theory, 15, 451-463 (1986; Zbl 0631.90106)].