Research On Guidance Strategy For Spacecraft Pursuit-Evasion Games

With the development of game theory in the space field,the spacecraft pursuit-evasion game has gradually become a research hotspot.The differential game is the basic theory to research on this issue,however the model based on differential game has some problems such as high sensitivity to the initial value,poor convergence and low solving efficiency.In this dissertation,based on the game theory which is combined with deep neural networks and pseudospectral method,the spacecraft pursuit-evasion games with different dynamics have been studied and the guidance laws are designed respectively.The main contributions of this dissertation are summarized as follows:Firstly,the dimension-reduction-DNN guidance method for nearly circular orbit pursuit-evasion game is proposed.In this method,the saddle-point strategies for the pursuer and evader are derived based on the differential game firstly.Then the costates are normalized to eliminate the uniqueness of solution and the DNNs are applied to approximate the reflection from the initial state to the solution.To improve the training efficiency,a closed-loop interactive structure is designed.Thus the trained DNNs can generate an initial solution when the initial state is given.To get an accurate solution,further optimization of outputs is implemented in neighboring regions.The numerical simulation demonstrates that the proposed method is feasible and the comparison with the referenced method displays the high efficiency and stability of this method.The results of Monte Carlo simulation show that the trained DNNs are robust when perturbed by the noise of the initial state.Secondly,the DNN-pseudospectral method for elliptical orbit pursuit-evasion game is proposed.To solve the problem,the dynamics of spacecraft is modelled by regrading the influence of eccentricity as a perturbation term.Then the saddle-point strategy is derived and an equivalent one-sided optimal control problem is constructed with the normalization of costates.The relationship between the initial state and the solution is learned by DNNs,and then the outputs of DNNs are taken as the initial guesses of Radau pseudospectral method and the quick convergence is achieved.The numerical simulation demonstrates that the derived one-sided optimal control problem is effective to solve the original problem and the comparison with the traditional method validates the high efficiency of the proposed method.Thirdly,the guidance strategy for spacecraft pursuit-evasion game with lin-earization error and J₂perturbation has been studied with two different methods.The first one is the combinatorial optimization method,and the second one is the ap-proximate solution based on Radau pseudospectral method.This problem is formulated and the saddle-point strategy is derived based on the differential game firstly.Then the combinatorial optimization method and the approximate solution based on Radau pseu-dospectral method are presented,respectively.In the combinatorial optimization method,the solution of the problem based on CW equation is integrated backward to generate the initial guess and the following optimization is utilized to get the accurate solution.In the approximate solution based on the Radau pseudospectral method,the pursuit-evasion game is transformed into two one-sided optimal control problems which are solved by the Radau pseudospectral method iteratively.The effectiveness of both methods are validated by the simulation results of three cases.Finally,the guidance method for spacecraft pursuit-evasion-defense game is proposed based on fuzzy comprehensive evaluation method.The concept of defender is introduced into the spacecraft pursuit-evasion game firstly,and the spacecraft pursuit-evasion-defense game is modelled.The original problem is transformed into a two point bound value problem,and the guidance laws of evader and defender are derived.Fur-thermore,the fuzzy comprehensive evaluation method is used to evaluate how threatened the pursuer is based on the real-time zero effort miss,then the guidance strategy of pur-suer is decided.The simulation results demonstrate that pursuer can capture the evader successfully while escaping from the defender by the proposed method.To summarize,this dissertation obtained the saddle-point guidance law for the space-craft pursuit-evasion game in four different scenarios respectively,which provides refer-ences for the following research and has the theoretical and practical significance.