Numerical solution for elliptical orbit pursuit-evasion game via deep neural networks and pseudospectral method

Abstract

This paper presents an efficient and stable DNNs-based Radau pseudospectral method for the free-time elliptical orbit pursuit-evasion game based on the equivalent reconstruction of the game model. Firstly, the relative dynamics equations are established by adding the nonlinear terms caused by the eccentricity to the Hill–Clohessy–Wilshire equations. Then the original pursuit-evasion problem is deduced to a 4-dimensional one-sided optimal control problem (OCP) based on the equivalent reconstruction. Secondly, in order to apply the deep neural networks (DNNs) to map the relationship between the OCP and the solution, the normalization of costates is introduced to eliminate the non-uniqueness of solutions when generating samples for training DNNs. Thirdly, the DNNs-based Radau pseudospectral method is proposed where the DNNs output the guesses of solutions to the derived OCP and the Radau pseudospectral method optimizes the histories of controls obtained by the guesses to the convergence. The simulation results demonstrate that the proposed method converges more stably and decreases the calculation time greatly compared with the traditional indirect method.