Numerical approaches to linear—quadratic differential games with imperfect observations

A two-person pursuit—evasion stochastic differential game with state and measurements corrupted by noises is considered. In an earlier paper the problem was reformulated and solved in an infinite-dimensional-state space, and the existence of saddle-point solutions under certain conditions was proved. The present paper provides a numerical solution for the resulting continuous-time integro-partial differential equations. This solution scheme is based on the utilization of the second guessing technique, and, in spite of the fact that a complicated set of integro-partial differential equations have to be solved, the numerical results seem plausible and promising.