Recent development of deep learning has shown that deep neural network (DNN) is capable of learning the underlying nonlinear relationship between the state and the optimal actions for nonlinear optimal control problems. In terms of hypersonic flight, this suggests that the DNN-based trajectory controller may be considered to take over all or part of the on-board trajectory generation and guidance system. In this work, we investigate the possibility of training the DNN-based controller off-line using the optimal state-action samples obtained from high-fidelity algorithms. The time-consuming computation is carried out off-line, and the resulting DNN-based controller is potentially capable of near-optimal control with realtime performance and stable convergence. First, the system dynamics of hypersonic flight are described, and the trajectory optimization problem is formulated as a highly nonlinear optimal control problem. Then, the state-action vectors are extracted from the optimal trajectories generated by solving the formulated optimal control problem from random initial states using a homotopy method. Thereafter, DNNs are designed to learn the functional relationship between the flight states and the optimal actions to enable the capability of optimal action predictions. At last, the performance of the proposed approach is demonstrated through numerical simulations.
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