Neural network based constrained optimal guidance for Mars entry vehicles

In this paper, an approximate constrained optimal guidance law is proposed for Mars entry vehicles guidance. Firstly, the original guidance of Mars entry vehicle is transformed into a fixed-time optimal tracking control problem, which depends on the solution of the Hamilton-Jacobi-Bellman (HJB) equation. Considering the case the control input is constrained, a generalized non-quadratic performance index is defined. In general, the HJB equation is a nonlinear partial differential equation that is difficult or even impossible to be solved analytically. To overcome the difficulty, neural network (NN) is used to solve the HJB equation approximately. Subsequently, the Monte-Carlo integration method and Latin Hypercube Sampling (LHS) are introduced to compute the integrals on multi-dimensional domains. Finally, the Monte-Carlo simulation results on the Mars entry vehicle demonstrate the effectiveness of the proposed method.