Research On Control Method For Spacecraft Pursuit-evasion Based On Differential Game Theory

With the increasing quantity of spacecraft in space and the increasingly intensified international competition,intentional and unintentional space threats are growing.In order to deal with space threats,this paper focuses on the research of spacecraft pursuit-evasion control methods and takes the differential game theory as the research tool.The deviations and failures of spacecraft control caused by the active defense,the motion state uncertainty,and the behavior information uncertainty are solved.This study has important theoretical value and practical engineering application value for improving the spacecraft’s space combat ability in the actual scene.The main research contents of this paper are as follows.In order to solve the problem that it is difficult for the pursuer to intercept the evader in the spacecraft pursuit-evasion-defense game,the pursuer’s control strategy is designed based on the fuzzy comprehensive evaluation method and the differential game theory.Firstly,the system dimension is reduced based on the zero-effort miss distance,and the pursuer’s combined objective function is designed based on the fuzzy comprehensive evaluation.Secondly,the original problem is transformed into a two-point boundary value problem based on the non-cooperative N-person differential game theory.Thirdly,a hybrid method combining differential evolution algorithm and multiple shooting method is proposed to solve the two-point boundary value problem.The optimal control strategy of the pursuer is obtained.Finally,the game results of the combined objective function and the single objective function are compared.The results show that the proposed control strategy can make the pursuer bypass the defender and capture the evader when the pursuer’s control is dominant and prolong the intercepting time when the pursuer’s control is not dominant.In order to construct an analytical form feedback control strategy in the bounded spacecraft pursuit-evasion game,a guaranteed cost strategy is proposed.The guaranteed cost strategy with unknown time-to-go is constructed based on Lyapunov-like function and matrix analysis theory.Then,a hybrid method combining the homotopy method and Newton’s method is proposed to calculate the unknown time-to-go.The results show that the proposed guaranteed cost strategy can effectively calculate the time-to-go of interception or escape and ensure the spacecraft achieve interception or escape within the corresponding time-to-go.In order to deal with the control deviation caused by information delay,a compensation control strategy is proposed based on the uncertainty set and the guaranteed cost strategy.Firstly,the delayed spacecraft pursuit-evasion problem is transformed into a typical spacecraft pursuit-evasion problem by replacing the delayed information with the spacecraft uncertainty set’s geometric center.Secondly,the construction method of guaranteed cost strategy is applied to the converted problem,and the compensation control strategy suitable for delayed spacecraft pursuit-evasion is obtained.The results show that the proposed compensation control strategy can effectively compensate part of the time delay and ensure the interception or escape within the predicted time-to-go under the condition that the delay time does not exceed the predicted maximum time.In order to reduce the control performance loss caused by switching and uncertainty of the behavior structure in the spacecraft pursuit-evasion with incomplete information,a multi-model behavior estimation method and a multi-stage adaptive control strategy are proposed.Firstly,the possible behavior model of the opponent is established through behavior analysis.An inverse dynamic problem solver is then established to calculate the historical control information based on the historical state information.Secondly,the parameters of each behavior model are estimated according to the state information and control information.Thirdly,the estimated behavior models are used to predict the opponent’s control value at the next moment,and the best behavior model is selected through comparison.Finally,a multi-stage adaptive control strategy is designed based on the best behavior model and the game process’s information.The results show that the proposed multi-model behavior estimation method can precisely estimate the opponent’s behavior model in various situations.The proposed multi-stage adaptive control strategy can effectively switch its control strategy according to the opponent’s behavior to reduce the performance loss in the game process.In order to deal with the control difficulty in the scene that active defense,state information uncertainty,and behavior information uncertainty exist simultaneously,a framework with modified algorithms is proposed.Firstly,a double-layer operating framework of inner and outer rings is designed to combine the proposed methods.Secondly,each method’s characteristics are analyzed,and two groups of reasonable limiting conditions are sorted out.Thirdly,some algorithms are modified according to the limiting conditions.Finally,the simulation analysis is carried out under two limited condition groups.The results show that the double-layer operating framework of inner and outer rings can effectively combine the algorithms under each factor.The spacecraft can effectively deal with various factors in the game to achieve its own game goals.