FORMAL SOLUTIONS FOR A CLASS OF STOCHASTIC PURSUIT-EVASION GAMES.

摘要

A class of differential pursuit-evasion games is examined in which the dynamics are linear and perturbed by additive white Gaussian noise,the performance index is quadratic,and both players receive measurements perturbed independently by additive white Gaussian noise. A direct application of the saddle point condition is used formally to characterize linear minimax solutions in terms of a system of implicit integro-differential equations,which appears to be more complicated than the ordinary kind of two point boundary value problem. It is also shown that games of this type posses a 'certainty-coincidence'property,meaning that their behavior coincides with that of corresponding deterministic games in the event that all noise values are zero. This property is used to decompose the minimax strategies into sums of a certainty-equivalent term and error terms. (Author)