Guaranteed cost tracking control of constrained input nonlinear uncertain systems using event-based ADP

Abstract

This article investigates the guaranteed cost robust tracking control problem of nonlinear systems subjected to input constraint and unmatched uncertainty. The event-based adaptive dynamic programming (ADP) approach is utilized to address this problem. First, the tracking error and reference trajectory are combined to form an augmented uncertain system. Then, by decomposing the uncertainty into the matched and unmatched parts, the original tracking problem is converted into the optimal regulation problem of an auxiliary system. The cost function for the auxiliary system is defined, and the associated Hamilton–Jacobi–Bellman (HJB) equation is solved using a single critic neural network (NN). Moreover, a novel event-triggering rule is formulated, and it is shown that the designed event-based controller guarantees that the tracking error is uniformly ultimately bounded. The derivation of event-based guaranteed cost and its relation with the time-based counterpart is presented. The exclusion of the infamous Zeno behavior is guaranteed. The uniform ultimate boundedness of the critic weight estimation error is shown. Finally, the effectiveness of the proposed event-triggered ADP method is illustrated through simulations of the spring–mass–damper system and Van der Pol’s oscillator with unmatched uncertainty.