Event-Triggered Robust Stabilization of Nonlinear Input-Constrained Systems Using Single Network Adaptive Critic Designs

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 50; no. 9; pp. 3145 - 3157
• Main Authors: Yang, Xiong, He, Haibo
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive critic designs (ACDs); adaptive dynamic programming (ADP); Adaptive systems; Constraints; Control systems; Cost function; event-triggered control (ETC); input constraints; neural network (NN); Nonlinear systems; Optimal control; Pendulums; Perturbation methods; reinforcement learning (RL); Robust control; Robust stabilization; Robustness
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2018.2853089

In this paper, we study the event-triggered robust stabilization problem of nonlinear systems subject to mismatched perturbations and input constraints. First, with the introduction of an infinite-horizon cost function for the auxiliary system, we transform the robust stabilization problem into a constrained optimal control problem. Then, we prove that the solution of the event-triggered Hamilton-Jacobi-Bellman (ETHJB) equation, which arises in the constrained optimal control problem, guarantees original system states to be uniformly ultimately bounded (UUB). To solve the ETHJB equation, we present a single network adaptive critic design (SN-ACD). The critic network used in the SN-ACD is tuned through the gradient descent method. By using Lyapunov method, we demonstrate that all the signals in the closed-loop auxiliary system are UUB. Finally, we provide two examples, including the pendulum system, to validate the proposed event-triggered control strategy.