Hybrid Event-Triggered Control with Stability Analysis

In this paper, a novel hybrid event-triggered control (ETC) method is developed based on the online action-critic technique, which aims at tackling the optimal regulation problem of discrete-time nonlinear systems. In order to ensure the normal execution of the online learning algorithm, a stability criterion condition is created to obtain the initial admissible control policy by using an offline iterative method under the time-triggered control framework. Subsequently, a general triggering condition is designed based on the uniform ultimate boundedness of the controlled system. In order to determine a constant interval which can ensure the system stability, another triggering condition is introduced and the asymptotic stability of the closed-loop system satisfying this condition is analyzed from the perspective of the input-to-state stability. The designed online hybrid ETC method not only further improves control efficiency, but also avoids the continuous judgment of the corresponding triggering condition. In addition, the event-based control law can approach the optimal control input within a finite approximation error. Finally, two experimental examples with physical background are conducted to indicate the present results.