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Dynamic Event-triggered Approximate Optimal Control Strategy for Nonlinear Systems

Songsong Cheng, Mingjian Zhu, Yuhui Fu, Xiaohan Fang, and Yuan Fan*
International Journal of Control, Automation, and Systems, vol. 20, no. 5, pp.1418-1427, 2022

Abstract : This work proposes a novel dynamic event-triggered approximate optimal control strategy for nonlinear continuous-time systems. By employing the dynamic event-triggered control scheme, the purposes of maintaining system stability, approximatly minimizing the cost function, and saving communication as well as computation resources can be achieved simultaneously. Firstly, to obtain the solution of the optimal control problem, we propose the Hamiltonian-Jacobian-Bellman (HJB) equation. A critic network is involved to approximate the optimal discounted cost function. A weight matrix update scheme using gradient descent method is designed to realize the weight calculation of the neural network. Secondly, a dynamic event-triggered condition has been presented to derive a near optimal event-triggered controller, which is more efficient in resource utilization than that of existing results. By using the Lyapunov method, it is proven that the states in the closed-loop system are uniformly ultimately bounded. Finally, numerical results and some comparison with the static ETM and time-triggered systems have been provided to illustrate the effectiveness of the proposed dynamic event-triggered mechanisms (ETM).

Keyword : Event-triggered control, Lyapunov method, neural networks, nonlinear systems, optimal control.

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