Optimal Strategy for Aircraft Pursuit-evasion Games via Self-play Iteration

In this paper, the pursuit-evasion game with state and control constraints is solved to achieve the Nash equilibrium of both the pursuer and the evader with an iterative self-play technique. Under the condition where the Hamiltonian formed by means of Pontryagin′s maximum principle has the unique solution, it can be proven that the iterative control law converges to the Nash equilibrium solution. However, the strong nonlinearity of the ordinary differential equations formulated by Pontryagin′s maximum principle makes the control policy difficult to figured out. Moreover the system dynamics employed in this manuscript contains a high dimensional state vector with constraints. In practical applications, such as the control of aircraft, the provided overload is limited. Therefore, in this paper, we consider the optimal strategy of pursuit-evasion games with constant constraint on the control, while some state vectors are restricted by the function of the input. To address the challenges, the optimal control problems are transformed into nonlinear programming problems through the direct collocation method. Finally, two numerical cases of the aircraft pursuit-evasion scenario are given to demonstrate the effectiveness of the presented method to obtain the optimal control of both the pursuer and the evader.