Nonzero-Sum Orbital Pursuit-Evasion Games Under Nonlinear Dynamics: A Derivative-Enhanced Differential Evolution Algorithm

This article focuses on a nonzero-sum orbital pursuit-evasion game (OPEG) with free terminal time. A nonlinear dynamics model for spacecraft is considered. The optimal conditions for the nonzero-sum OPEG are derived, which can be mathematically expressed as a high-dimensional two-point boundary value problem (TPBVP). Based on the properties of the coefficient matrices, the dimension of the TPBVP is reduced and it is transformed into an optimization problem. The optimization problem aims to find the optimal initial boundary of the TPBVP that satisfies the optimal conditions, which is challenging to solve due to the nonlinearity and the nonconvexity brought by the dynamics. A derivative-enhanced differential evolution algorithm is then proposed, taking both the global search ability and the convergence speed into consideration. Finally, some simulations for the nonzero-sum and the zero-sum cases are provided to show the robustness of the algorithm. It is demonstrated that the algorithm has better efficiency, accuracy, and stability compared with the existing algorithms.