Dynamic event-triggered optimal critic-only control strategy for nonlinear systems based on state observer

This paper develops a dynamic event-triggered optimal control method based on a critic neural network (CNN) for nonlinear continuous-time (CT) systems with a state observer. Firstly, a discounted cost function is introduced to solve the optimal problem of the nonlinear systems, and the related optimal performance index function and a Hamilton-Jacobi-Bellman (HJB) equation are established to obtain the optimal control law. Then, to reduce communication burdens, a dynamic event-triggered control (DETC) method is defined by adding an additional dynamic variable on the basis of the traditional event-triggered control (ETC) method to keep the aperiodic update of the systems, and the stability of the systems based on these two methods are proved, respectively. Moreover, to approximate the optimal solution of the HJB equation, a CNN is utilized to approximate the optimal performance index function and tune its weight by the gradient descent approach. By the Lyapunov method, the uniform ultimate boundedness (UUB) of the closed-loop systems is proved, while also excluding Zeno behavior. Finally, the effectiveness of the proposed optimal control strategy is verified by two simulations.