Stochastic Differential Game Techniques

Abstract

Abstract : This development of readily computable strategies for differential games with noise corrupted measurements was hampered by the so called closure problem of stochastic differential games. The solutions required either an infinite dimensional dynamic system or the determination at each time t of the error in the opponent's state estimate. In this dissertation, solutions to different games with noise corrupted measurements were obtained that are readily computable. As a consequence of the stochastic aspects of such games, the discussion was restricted to linear-quadratic differential games which are analyzed using function space techniques. The solution to a linear-quadratic game with perfect information is obtained without the a prior assumption of a saddle-point solution and it is shown that the individual minimax and miximin solutions to such a game result in a set of strategies that satisfy the saddle-point condition, but with necessary and sufficient conditions that are more stringent than previously obtained. The concept of delayed commitment games is then extended to differential games where both players have noise corrupted state measurements and solutions are obtained that are readily computable, thus playing to rest the closure problem of stochastic differential games.