Novel Approaches to Stochastic Pursuit-Evasion Differential Games with multiple players

We propose to systemically explore differential pursuit-evasion games with multiple pursuers and evaders in continuous time and in random environment. We start with the simplest case with the assumptions of perfect information and common knowledge. The approach is a direct extension of Isaacs's method for differential games with a single pursuer and evader, where the concept of saddle point solutions is extended. Second, the assumption of perfect information is relaxed to that of complete observability. To simplify the theoretical analysis, a transformation of the objective function is considered such that the linear quadratic dynamic game theory can be applied directly. Asymptotic Nash equilibrium solutions can be easily determined in this case. Third, the assumptions of observability and common knowledge are further relaxed, the learning theory in games is proposed. In this case, a larger set of self-confirming equilibrium solutions is used to instead of Nash equilibrium. Fourth, for the situation that players cannot predict others' strategies, a decentralized objective function is constructed for each pursuer, and the maxmin strategy is proposed. The coordination control is achieved by using maximal Nash equilibrium solution among those distributed pursuers. Finally, a general nonlinear filter is proposed for each pursuer to estimate the observable state variables in noisy environment.