Strategy and numerical solution of pursuit-evasion with fixed duration for two spacecraft

For the problem of pursuit-evasion with fixed duration for two spacecraft, an optimal control strategy and its numerical solution method are investigated based on the differential game theory. The two spacecraft are conflicted with each other under the assumed condition of low continuous thrust in a dynamics system with time-dependent angular velocity and trajectory altitude. The terminal distance is taken as a payoff. The pursuer tries to minimize the payoff, and the evader tries to maximize it. Consequently, a high-order time-dependent nonlinear two-point boundary-value problem is introduced by using the necessary condition of the differential game. In this paper, a hybrid algorithm is presented by combining the multiple-shooting method with the genetic algorithm for solving this type of pursuit-evasion problem. In this hybrid algorithm, an improved multi-objective genetic algorithm is adopted to obtain the initial estimation of the costate variables, and the result of the genetic algorithm is used as a feeder for the multiple shooting method to solve the solution of the complex two-point boundary-value problem. It is shown by the simulations that this hybrid algorithm has guarantee accuracy and robustness for the problem. Simultaneously, the optimal strategies and the corresponding pursuit-evasion trajectory are obtained.