State-Feedback Equilibrium Strategy for a 3-D Inertial Game With Two Cooperative Pursuers Versus One Superior Evader

Differential games featuring multiple weak pursuers against a highly maneuverable evader are critical in aerospace applications, yet remain inherently complex and challenging. In this study, we examine a scenario involving two cooperative weak pursuers and a superior evader, with all participants modeled by inertial dynamics during high-speed encounters. We derive the value function using reachable sets and accordingly propose an open-loop Stackelberg state-feedback strategy. Furthermore, we demonstrate that this strategy constitutes a Nash equilibrium in the closed-loop game over the entire state space by showing that the pursuers’ strategy guarantees that the payoff function is less than or equal to the value function, while the evader’s strategy guarantees that payoff function is greater than or equal to the value function. Simulation results are provided, which corroborate our theoretical analysis.