Research On Control And Solving Method Of Pursuit-Evasion Gmae For Spacecraft

Considering the requirements for application of online solving and the problem that most of computation intensive methods hold low efficiency in spacecraft pursuitevasion game,this article does research into two typical spacecraft pursuit-evasion games and proposes corresponding high efficiency numerical methods.Furthermore,the validity and feature of the game is verified and analyzed.Main contributions of this thesis are presented as follows:For the interception scene,a game model with linear quadratic payoff is established and a feedback control law is derived.The gain matrix of the feedback control law is obtained by solving a Matrix Riccati Differential Equation.To improve the efficiency,a semi-analytical method is proposed in which the method converts the nonlinear Matrix Riccati Differential Equation into a linear first-order ordinary differential equation base on inverse riccati matrix,and obtains an analytic solution of the inverse riccati matrix by symbol-solving tool.Then the riccati matrix is obtained by numerical inversion for the inverse riccati matrix.Significance of the method is that the complex numerical integration calculation of the high-dimensional equations is simplified to a calculation of inversion,in which the computation is effectively reduced.The validity is verified by a comparison between the game control law and a common control law.Besides,a superior-condition of the evader is discussed,and a control threshold formula is derived which describes the condition how the evaders can obtain advantages.For the capture scene,the game is considered as a survival game model where the goal of a pursuer is to achieve its capture objective as soon as possible and an evader aims to prolong it.The pursuit-evasion-capture game can be converted as a TPBVP in which the key point is to solve a nonlinear equation.Shooting method is taken to solve the problem because of its high accuracy and fast convergence.Progressive Shooting Method is proposed in this paper.The method solves the problem in two stages: first-shooting and second-shooting.First-shooting settles a simplified problem by substituting CW dynamics to simple dynamics,while secondshooting settles the original problem with the results of first-shooting.For firstshooting,an analytic construction method for an initial guess based on prior information is proposed,in which vague adjoint variables are expressed by quantities with clear physical meanings.Through qualitative analysis for the optimal trajectory,the quantities are approximately estimated and then analytic expressions of an initial guess are constructed.Numerical results show that a class of typical scene can be stably solved by Progressive Shooting Method and the constructed initial guess with well applicability and high efficiency.