Pursuit-evasion game with delayed pursuit decision

A pursuit-evasion differential game problem involving a single pursuer and multiple evaders is considered. At a prescribed moment, the pursuer chooses a single evader for interception. It is assumed that the probabilities of choosing each of the evaders are known. The strategies after the decision time are known yielding a performance index depending on the state at the decision time. A differential game problem before the decision time is formulated that takes into account the average performance over all decision outcomes. Based on this differential game formulation, we derive a guidance algorithm and study its performance under different situations using numerical simulations. The game solvability conditions are established. The influence of control effort penalty coefficients on the pursuit strategy performance is investigated. Numerical simulation results are presented.