A hybrid optimisation method for intercepting satellite trajectory based on differential game

This study addresses orbit design and optimisation for the situation of satellite interception in which the target spacecraft is capable of manoeuvring using continuous magnitude restricted thrust. For the purpose of designing a long-range continuous thrust interception orbit, the orbit motion equations of two satellites with J2 perturbation are constructed. This problem is assumed to be a typical pursuit-evasion problem in differential game theory; using boundary constraint conditions and a performance index function that includes time and fuel consumption, the saddle point solution corresponding to the bilateral optimal is derived, and then this pursuit-evasion problem is transformed into a two-point boundary value problem. A hybrid optimisation method using a genetic algorithm (GA) and sequential quadratic programming (SQP) is derived to obtain the optimal control strategy. The proposed model and algorithm are proved to be feasible for the given simulation cases.