Optimal tracking control for unknown nonlinear systems with uncertain input saturation: A dynamic event-triggered ADP algorithm

This paper is devoted to proposing a novel dynamic event-triggered adaptive dynamic programming (ADP) algorithm to tackle the tracking control problem of unknown nonlinear systems with uncertain input saturation. Initially, an augmented system is established to address the investigated optimal tracking control issue with a discounted cost function. An online identifier based on neural networks (NNs) is designed to recover the unknown system dynamics. Furthermore, the controller design consists of two parts, including the optimal control policy for the nominal system and the NN-based feedforward compensator. In particular, the latter leverages adaptive NN techniques to cope with uncertain input constraints which can be deemed as uncertain saturation nonlinearities. A critic NN is constructed to obtain the approximate optimal control policy for the nominal system. Moreover, rather than traditional time-triggered and static event-triggered control schemes, an adaptive dynamic event-triggering condition is designed to determine the system sampling as well as the controller execution to further reduce transmission and computation burden. The introduction of an internal dynamic variable in possession of a positive constant lower bound can realize the dynamic adjustment of triggering threshold and effectively exclude Zeno behavior. Notice that the weights of identifier NN and critic NN are updated simultaneously, only at the event-triggering instants. Subsequently, the Lyapunov-based theoretical analysis is conducted to confirm the uniform ultimate boundedness of the tracking error and all the NN weight estimation errors. Eventually, the feasibility and effectiveness of the developed algorithm are validated by means of two simulation examples.