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

Abstract

In this paper, 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.