A Payoff Augmentation Approach to Two Pursuers and One Evader Inertial Model Differential Game

In this article, we study the two-on-one inertial model pursuit-evasion differential game with a payoff augmentation approach. In particular, the pursuit-evasion game is treated as a deadline game, and its payoff function is augmented to eliminate the deadline as well as to facilitate a more sophisticate model. In addition, we introduce the retrogressive path for analytical solution to the equilibrium strategy for the closed-loop game, and proceed to demonstrate that the closed-loop game can be converted to a one-side optimization problem for the evader, with the help of the augmented payoff function, under an open-loop Stackelberg strategy. More specifically, we establish the conditional equivalency between the open-loop solution and the closed-loop one. Simulation results verify the effectiveness of the proposed strategy.