Low-Thrust Trajectory Optimization via Knowledge-Enhanced Deep Neural Network

This paper introduces the warm restart approach with a knowledge-enhanced deep neural network for solving the low-thrust trajectory optimization problem, where a variable preprocessor, a warm initiator, and an exact solver are developed and cooperatively utilized in the warm restart framework. For the warm initiator, the sample form incorporating homotopic parameter is firstly designed to greatly improve sample generation efficiency and convenience. Additionally, a knowledge-enhanced training strategy utilizing the residual of the nonlinear equations as the loss function is proposed to achieve efficient training and accurate approximation of deep neural network while maintaining acceptable time and computational costs. For the exact solver, an adaptive homotopy coefficient solver with the adaptive step size adjustment strategy is presented to balance the solution time and success. Application results in the Jovian system demonstrate significant improvement in the accuracy and reliability of the deep neural network following enhanced training. The results of comparative simulations further verify that the proposed method exhibits remarkable advantages in terms of computational efficiency and stability for both time-optimal and fixed-time fuel-optimal low-thrust trajectory optimization problems.