Event-Based Robust Control for Uncertain Nonlinear Systems Using Adaptive Dynamic Programming

In this paper, the robust control problem for a class of continuous-time nonlinear system with unmatched uncertainties is investigated using an event-based control method. First, the robust control problem is transformed into a corresponding optimal control problem with an augmented control and an appropriate cost function. Under the event-based mechanism, we prove that the solution of the optimal control problem can asymptotically stabilize the uncertain system with an adaptive triggering condition. That is, the designed event-based controller is robust to the original uncertain system. Note that the event-based controller is updated only when the triggering condition is satisfied, which can save the communication resources between the plant and the controller. Then, a single network adaptive dynamic programming structure with experience replay technique is constructed to approach the optimal control policies. The stability of the closed-loop system with the event-based control policy and the augmented control policy is analyzed using the Lyapunov approach. Furthermore, we prove that the minimal intersample time is bounded by a nonzero positive constant, which excludes Zeno behavior during the learning process. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed control scheme.