Optimal Control Of Spacecraft Orbital Pursuit-evasion Based On Differential Game

Under the background of future security defense of on-orbit spacecraft,this dissertation studies the spacecraft orbital pursuit-evasion problems based on differential games theory.The pursuit-evasion models are established and an analytic solution of the barrier is proposed.Moreover,the approaches for finding the saddle point of orbital pursuit-evasion games are developed and the optimal control law with incomplete information is designed.The main achievements of this dissertation are summarized as follows.An analytic solution of the barrier in spacecraft orbital pursuit-evasion problems and a method for locating the capture-escape region are proposed.1)By approximating the control of the pursuer and evader using a polynomial in time-to-go ?,the analytic solution of the pursuit-evasion barrier is derived.2)Based on the analytic solution of barrier,a method for locating the capture-escape region in spacecraft orbital pursuit-evasion games is proposed by solving a minmax relative distance game problem.3)The characteristics of the barrier in orbital pursuit-evasion are analyzed,and the results show that it is anti-symmetric about the x axis.The solving approaches for the saddle point in spacecraft pursuit-evasion games are developed,and the characteristics of orbital pursuit-evasion are analyzed.1)Based on linear quadratic two-player zero-sum differential games theory,the solving approaches for the saddle point in spacecraft pursuit-evasion games with fix duration and infinite planning horizon are proposed,which reduce to solve a matrix Riccati differential equation(RDE)and a algebraic Riccati equation(ARE).2)In terms of the orbital survival pursuit-evasion games,we prove that the optimal controls of the pursuer are the same as that of the evader by using the necessary conditions of the saddle point.Then a fourth-order nonlinear equation are formulated to find the saddle point,which are further solved using a proposed hybrid algorithm combining differential evolution algorithm with Newton's iteration method.3)Three cases are presented to test the proposed methods and analyze the characteristics of orbital pursuit-evasion using three different models.The simulation results show that the conflict of the pursuer and evader is more intense in orbital plane while it tends to be mild out of orbital plane.The optimal control law of the pursuer in spacecraft orbital pursuit-evasion games with incomplete information is designed.1)The effects of incomplete information on pursuit-evasion games and the payoff of the pursuer are analyzed.2)From the view of the pursuer,an online estimation method of the incomplete information is proposed and the optimal control law in orbital pursuit-evasion is designed.3)The simulation results show that the proposed methods was able to increase the pursuer's performance in orbital pursuit-evasion with incomplete information.The proposed models and solving approaches of the optimal control strategies in spacecraft orbital pursuit-evasion games are theoretically of significance.Moreover,the analysis of the characteristics of orbital pursuit-evasion could provide valuable references for future counter-space missions,which is much of value in engineering practice.