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

For nonlinear Ito-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 Ito-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.

Automated summary

This paper investigates the event-triggered optimal control (ETOC) for nonlinear Ito-type stochastic systems using the adaptive dynamic programming (ADP) approach. The value function of the Hamilton-Jacobi-Bellman (HJB) equation is approximated using critical neural network (CNN), and a new event-triggering scheme is proposed. The Lyapunov direct method is used to prove that the ETOC based on ADP approach guarantees that the CNN weight errors and system states are semi-globally uniformly ultimately bounded in probability.