A Differential Game with Graph Constrained Switching Strategies

Abstract

A two-person zero-sum differential game of finite horizon with graphconstrained control strategies is adressed where both players are constrained to use piecewise constant controls, and the control switches are selected from a finite control graph. The control graph is a directed graph where the vertices define pairs of control values for both players, and the edges define the allowable control switches. A positive switching cost is associated with each edge, being the payoff function defined by the sum of the switching costs associated with each player. Issues concerning both the existence of value of the game and optimality conditions are addressed. in terms of value functions. Optimal strategies are derived in terms of a value functions which solve a coupled system of quasi-variational inequalities.