Event-triggered optimal control for nonlinear stochastic systems via adaptive dynamic programming

• Published in: Nonlinear dynamics Vol. 105; no. 1; pp. 387 - 401
• Main Authors: Zhang, Guoping, Zhu, Quanxin
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.07.2021; Springer Nature B.V
• Subjects: Adaptive systems; Artificial neural networks; Automotive Engineering; Classical Mechanics; Control; Cost function; Dynamic programming; Dynamical Systems; Engineering; Liapunov direct method; Mechanical Engineering; Nonlinear control; Nonlinear systems; Optimal control; Original Paper; Stochastic systems; Upper bounds; Vibration; Nonlinear Itô-type stochastic systems; Neural network; Event-triggered control; Optimal control; Adaptive dynamic programming (ADP); Hamilton–Jacobi–Bellman (HJB) equation
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-021-06624-8

For nonlinear Itô-type stochastic systems, the problem of event-triggered optimal control (ETOC) is studied in this paper, and the adaptive dynamic programming (ADP) approach is explored to implement it. The value function of the Hamilton–Jacobi–Bellman(HJB) equation is approximated by applying critical neural network (CNN). Moreover, a new event-triggering scheme is proposed, which can be used to design ETOC directly via the solution of HJB equation. By utilizing the Lyapunov direct method, it can be proved that the ETOC based on ADP approach can ensure that the CNN weight errors and states of system are semi-globally uniformly ultimately bounded in probability. Furthermore, an upper bound is given on predetermined cost function. Specifically, there has been no published literature on the ETOC for nonlinear Itô-type stochastic systems via the ADP method. This work is the first attempt to fill the gap in this subject. Finally, the effectiveness of the proposed method is illustrated through two numerical examples.