Adaptive Optimal Tracking Control for Spacecraft Formation Flying With Event-Triggered Input

This article addresses the event-triggered optimal tracking control problem for leader-follower spacecraft formation flying system using the adaptive dynamic programming technique. In order to solve the Hamilton–Jacobi–Bellman equation, a single-critic neural network (NN) is developed to approximate the optimal cost function. Moreover, by combining the parameter projection rule and gradient descent algorithm, a semiglobal adaptive update law is derived to tune the critic NN. In doing so, a continuous near optimal tracking controller is presented. Subsequently, an input-state-dependent event-triggered mechanism is designed to ensure that the near optimal tracking controller is implemented only when specific events occur, which significantly reduces the execution frequency of the control command. Remarkably, benefiting from the construction of an input-based triggering error, the conventional assumption on the Lipschitz continuity of the controller is tactfully removed, thus erasing the computable demand on the unknown Lipschitz constants. Rigorous analysis on the system stability and Zeno-free behavior is provided successively. Finally, numerical simulations on two formation satellites in low Earth orbit validate the effectiveness of the theoretical scheme.