Real-time optimal control for attitude-constrained solar sailcrafts via neural networks

Abstract

This work is devoted to generating optimal guidance commands in real time for attitude-constrained solar sailcrafts in coplanar circular-to-circular interplanetary transfers. Firstly, a nonlinear optimal control problem is established, and the necessary conditions for optimality are derived by Pontryagin’s Minimum Principle. Under some mild assumptions, the attitude constraints are rewritten as control constraints, which are replaced by a saturation function so that a parameterized system is formulated. This allows one to generate an optimal trajectory via solving an initial value problem, making it efficient to collect a dataset containing optimal samples, which are essential for training Neural Networks (NNs) to achieve real-time implementation. However, the optimal guidance command may suddenly change from one extreme to another, resulting in discontinuous jumps that generally impair the NN’s approximation performance. To address this issue, we use two co-states that the optimal guidance command depends on, to detect discontinuous jumps. A procedure for preprocessing these jumps is then established, thereby ensuring that the preprocessed guidance command remains smooth everywhere. Meanwhile, the sign of one co-state is found to be sufficient to revert the preprocessed guidance command back into the original optimal guidance command. Furthermore, three NNs are built and trained offline, and they cooperate to precisely generate the optimal guidance command in real time. Finally, numerical simulations are presented to demonstrate the developments of the paper.