Self-triggered adaptive dynamic programming based on experience-replay and spectral adaptive law

In this paper, a novel self-triggered adaptive dynamic programming (ADP) framework is proposed, integrating experience replay (ER) and a spectral adaptive law (SPAL) for optimal control of unknown nonlinear systems. Firstly, in ADP-based optimal control solution methods, a critic neural network (NN) is often used to approximate its cost function, and we design a new critic NN weight updating law based on the SPAL, which improves the system's generalization ability and makes it possible to solve the optimal control problem efficiently with different initial values. Then, a robust ADP method based on the ER technique is proposed in which a SPAL-based NN system identifier is used to provide data for ER, which systematically enhances the robustness of the ER-based ADP framework. Finally, since the sensors in the event-triggered ADP-based approach require continuous monitoring of the system state to compute the triggering conditions, to avoid this problem, we use a self-triggered mechanism that allows direct prediction of the next triggering moment based on the current state. The effectiveness and communication conservation of the proposed algorithm are verified by a simulation experiment.