Pursuit-evasion Strategies And Its Numerical Solution For Two Low-earth-circular-orbit Spacecraft With Saturation Function Thrust

Based on differential game theory, this paper mainly studies low earth circularorbit pursuit-evasion game of two spacecraft, where the control variable existsconstraints. The constraints of control variable can be realized by introducing asaturation function. Within the prescribed time, numerical results by using nonlinearprogramming algorithm will investigate whether the constraints is feasible with therelative distance and the energy consumption of two spacecraft as a payoff.According to the research content, this paper roughly divides into two parts. Thefirst part mainly introduces the origin and development of differential game andscholars’ achievements in this field both at home and abroad also the researchbackground and purpose of this article. In the second part, a detailed description ofestablishing countermeasure system and solving it through numerical methods is given.In the process of establishing countermeasure system, the relative coordinates isused. Based on two-body problem only in the role of gravity, the relative motionequations of two spacecraft can be deduced, thus further the kinetic equation of relativemotion between them is derived. Finally the system is established. With introducingstate transition matrix we can reduce the dimensions of the system, then we transformthe after reduction system into an optimal control problem based on optimal controltheory. Due to the high nonlinear degree of the optimal control problem, so we considerusing numerical method to get the solution. Then we use bvp4c solver of solvingtwo-point boundary value problem to do numerical simulation in the commonmathematical software MATLAB.Finally, through the analysis of three different numerical simulations results, it iseffective and feasible that the control variable with saturation function constraintsbesides it is in line with the actual situation.