A cyclic differential evolution framework for constrained orbital pursuit-evasion games

Orbital pursuit-evasion games have been widely studied, but most of the research is based on the assumption of no process constraints. For orbital pursuit-evasion games subject to orbital height constraints, the conditions for the existence of saddle points are derived. Based on the properties of the coefficient matrix, the equations are decoupled and reduced in dimension to two two-point boundary value problems (TPBVPs). The penalty function method is used to handle process constraints, and the two TPBVPs are then transformed into an optimization problem for the optimal conditions. This paper proposes a cyclic differential evolution framework for solving this optimization problem and conducts simulation. The simulation results verify the efficiency and accuracy of the framework, and reveal the practical significance of orbital height constraints for preventing collisions between spacecraft and the Earth.