Discontinuous differential games and control systems with supremum cost

This paper concerns with the existence of a value for a zero sum two-player differential game with supremum cost of the form Ct0,x0(u, v) = supτ ∈[t0,T ] h(x(τ ; t0,x0,u, v)) under Isaacs’ condition. We characterize the value function as the unique solution—in a suitable sense—to a PDE, namely the Hamilton–Jacobi–Isaacs equation. As a byproduct, we obtain a PDE characterization of the value function for control system.  2002 Elsevier Science (USA). All rights reserved