Optimal design of spacecraft low-thrust transfer orbit based on HJB-INN

<p indent="0mm">In view of the problems of difficult optimality guarantee, low computational efficiency and high initial value dependence in traditional continuous low thrust transfer optimization methods, a solution framework based on Hamilton-Jacobi-Bellman equations informed neural network (HJB-INN) is proposed in this paper. Firstly, the optimal control problem of spacecraft low thrust transfer under various scenarios is modeled, and a multi-constraint optimization problem model around affine nonlinear system is established; then, the Hamilton-Jacobi-Bellman equations under terminal constraints and control amplitude constraints are derived, and the closed-loop optimal control law is designed based on the value function; in order to solve the value function that satisfies the partial differential equations and boundary conditions, a network model integrating the theory of functional connections (TFC) and the extreme learning machine (ELM) in the spherical coordinate system is designed, and a grid update strategy is established to improve the overall accuracy. Simulation results indicate that the proposed method is capable of determining transfer orbits under multiple constraints. When compared to classical physics-informed neural network, the proposed approach exhibits superior solution accuracy. Moreover, as it approaches the theoretical optimal value, this method demonstrates reduced sensitivity to initial values relative to traditional direct and indirect methods. Consequently, this approach is well-suited for the optimization design of continuous low-thrust transfer orbits in spacecraft, offering a promising alternative for trajectory planning.