In this study, an intelligent predictor-corrector entry guidance approach for lifting hypersonic vehicles is proposed to achieve real-time and safe control of entry flights by leveraging the deep neural network (DNN) and constraint management techniques. First, the entry trajectory planning problem is formulated as a univariate root-finding problem based on a compound bank angle corridor, and two constraint management algorithms are presented to enforce the satisfaction of both path and terminal constraints. Second, a DNN is developed to learn the mapping relationship between the flight states and ranges, and experiments are conducted to verify its high approximation accuracy. Based on the DNN-based range predictor, an intelligent, multi-constrained predictor-corrector guidance algorithm is developed to achieve real-time trajectory correction and lateral heading control with a determined number of bank reversals. Simulations are conducted through comparing with the state-of-the-art predictor-corrector algorithms, and the results demonstrate that the proposed DNNbased entry guidance can achieve the trajectory correction with an update frequency of 20 Hz and is capable of providing highprecision, safe, and robust entry guidance for hypersonic vehicles.

Although the robustness of indirect methods is enhanced by the homotopic approach and switching detection technique when applied to fuel-optimal low-thrust trajectory optimization, the bottleneck in adjoint initialization still needs further investigation. This paper overcomes this bottleneck by the adjoint mapping between the Lagrange multipliers of direct methods to the adjoint variables. The nonconvex optimization problem deduced from direct methods is converted into a convex one by lossless convexification and successive convex programming. By combining these techniques, a framework is built to effectively solve the fuel-optimal low-thrust trajectory optimization problem.

To improve the autonomy and reliability of asteroid landings, an intelligent approach to fast and reliable generation of optimal landing trajectories is proposed. Unfortunately, the indirect methods require good initial guesses for shootings. To address this issue, deep neural networks (DNNs) are developed to approximate the costates of the indirect methods and supply good initial solutions to achieve high success rate of shootings. This article focuses on the following three contributions. First, the original asteroid landing problems are connected with two-dimensional (2-D) asteroid-free transfer problems using model continuation and state transformation techniques. Second, DNNs are developed and optimized to approximate the costates of the 2-D transfers with high accuracy. Third, a systematical solution for asteroid landing trajectory optimization is developed, wherein the DNNs provide good initial solutions, and the accurate solutions for landings are obtained through a solution continuation process. Additionally, an alternative solution supplying strategy based on error statistics of DNN approximation is presented to take over the solution supplying when the predictions of DNNs fail to converge to the optima. Evaluations of the DNNs for solution supplying and simulations of landings on 433 Eros and 101955 Bennu are given to substantiate the effectiveness of the proposed techniques and demonstrate the performance of the developed algorithm.