On the value of differential game with asymmetric control constraints

Abstract

A differential game with asymmetric constraints on the players’ controls and an asymmetric cost functional is considered. In this game hard geometric constraints are imposed on the maximizer, whereas the minimizer is soft-constrained by including the control effort term into the cost functional. The sufficient condition is derived, subject to which the program maximin is the game value. In the proof, it is shown that the program maximin is the generalized solution of the Hamilton-Jacobi-Bellman partial differential equation. Examples are presented. © 2018