Pursuit Evasion Game with J2 Perturbation

A two-side optimization problem where the intercepting satellite pursued the target satellite was studied in this paper. In the pursuit-evasion game, it was assumed that both sides use the continuous thruster and suffer from the earth central gravity with J2 perturbation. The dynamics equations were established to describe their three dimensional motion. Then the optimal control outputs of both side satellites were obtained by building the systems Hamilton and applying the functional extremal condition. The pursuit evasion games was transformed to the two point boundary value problem. At last the new problem was solved with the mixed numerical method where an initial solution was acquired by the genetic algorithm and sent to nonlinear programming as its starting value. Simulation was used to obtain the optimal interception and escaping trajectories of the two satellites and validate the proposed method.