Impulsive thrust strategy for orbital pursuit-evasion games based on impulse-like constraint

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This paper proposes a novel impulsive thrust strategy guided by optimal continuous thrust strategy to address two-player orbital pursuit-evasion game under impulsive thrust control. The strategy seeks to enhance the interpretability of impulsive thrust strategy by integrating it within the framework of differential game in traditional continuous systems. First, this paper introduces an impulse-like constraint, with periodical changes in thrust amplitude, to characterize the impulsive thrust control. Then, the game with the impulse-like constraint is converted into the two-point boundary value problem, which is solved by the combined shooting and deep learning method proposed in this paper. Deep learning and numerical optimization are employed to obtain the guesses for unknown terminal adjoint variables and the game terminal time. Subsequently, the accurate values are solved by the shooting method to yield the optimal continuous thrust strategy with the impulse-like constraint. Finally, the shooting method is iteratively employed at each impulse decision moment to derive the impulsive thrust strategy guided by the optimal continuous thrust strategy. Numerical examples demonstrate the convergence of the combined shooting and deep learning method, even if the strongly nonlinear impulse-like constraint is introduced. The effect of the impulsive thrust strategy guided by the optimal continuous thrust strategy is also discussed.