EXISTENCE OF THE VALUE FOR A DIFFERENTIAL GAME WITH SWITCHING STRATEGIES IN A BANACH SPACE

A two-player zero-sum differential game in some Banach space is studied.Positiveswitching costs are associated with each player.By regularizing the game and combining thenotion of viscosity solutions for Isaacs-Bellman equation,we obtain the existence of the Elliot-Kalton value of the game under suitable conditions.     

OPTIMAL SWITCHING AND IMPULSE CONTROLS FOR DISTRIBUTED PARAMETER SYSTEMS

Optimal switching and impulse controls for a distributed parameter systems are considered.We prove that the value functions u_u(·) of approximating problems approach to the value functionu(·) of the original problem,while u_u(·) is the unique viscosity solution of the correspondingHamilton-Jacobi-Bellman system.We also construct an optimal control for the original problem viathe value function u(·).