Robust tracking control of nonlinear unmatched uncertain systems via event-based adaptive dynamic programming

In this paper, a novel robust tracking control strategy for nonlinear unmatched uncertain systems is formulated using the event-based adaptive dynamic programming (ADP) approach. First, an augmented system is constructed based on the nonlinear system and the reference trajectory. Then, by forming an auxiliary system and introducing a discounted cost function, the event-based robust tracking control problem is transformed into the event-based optimal control problem of the auxiliary system. The event-based Hamilton-Jacobi-Bellman (HJB) equation associated with the event-based optimal control problem is solved using a single critic neural network (NN) under the ADP framework. A novel weight tuning rule for the critic network is formulated to avoid the necessity of an initial admissible control at the beginning of the weights tuning process. The obtained event-based controller is updated only at the triggering instants decided by the designed triggering condition, which helped in a significant reduction of resources used in computation and communication. Meanwhile, it is demonstrated that the obtained event-based controller can guarantee the tracking error's uniform ultimate boundedness. Furthermore, using the Lyapunov method, it is guaranteed that the established novel event-triggering rule ensures uniform ultimate boundedness of all signals associated with the closed-loop auxiliary system. Finally, the applicability of the proposed control scheme is demonstrated by providing two simulation examples.