On Mixed Data and Event Driven Design for Adaptive-Critic-Based Nonlinear $H_{\infty}$ Control

Abstract

In this paper, based on the adaptive critic learning technique, the control for a class of unknown nonlinear dynamic systems is investigated by adopting a mixed data and event driven design approach. The nonlinear control problem is formulated as a two-player zero-sum differential game and the adaptive critic method is employed to cope with the data-based optimization. The novelty lies in that the data driven learning identifier is combined with the event driven design formulation, in order to develop the adaptive critic controller, thereby accomplishing the nonlinear control. The event driven optimal control law and the time driven worst case disturbance law are approximated by constructing and tuning a critic neural network. Applying the event driven feedback control, the closed-loop system is built with stability analysis. Simulation studies are conducted to verify the theoretical results and illustrate the control performance. It is significant to observe that the present research provides a new avenue of integrating data-based control and event-triggering mechanism into establishing advanced adaptive critic systems.

A mixed PI/VI design method for nonlinear H∞ Control

“…The following Hamilton-Jacobi inequality (14) can be driven from the HJI equation. According to theorem 16 in the work of van der Schaft, 1 if the Hamilton-Jacobi inequality (14) holds for a given > 0, then NHCPS are also achieved.…”

“…If (x) ≤ 0 holds, then x T (x)x ≤ 0, which implies that inequality (14) holds. Hence, NHCPS are achieved for a given > 0.…”

“…Wang et al studied the solution of the HJI equation via ADP and developed an event‐based input‐constrained H ∞ control method. In addition, they improved the adaptive critic technique and the adaptive critic learning technique . Zhang et al studied the design of the nonlinear H ∞ control by using both RL and ADP for nonlinear systems with input saturation and disturbance.…”

“…In addition, they improved the adaptive critic technique 13 and the adaptive critic learning technique. 14 Zhang et al 15-19 studied the design of the nonlinear H ∞ control by using both RL and ADP for nonlinear systems with input saturation and disturbance. Yang et al 20-23 Zhang et al, 24 and Zhu et al 25 studied the design of the nonlinear H ∞ control for nonlinear systems with special properties, such as constrained-input systems, 20 mismatched disturbances, 21,22 event-triggered control algorithms, 23,24 and polynomial nonlinear systems.…”

A simple nonlinear H∞ control design method: Polynomial nonlinear control

“…In the work of Wang et al, an event‐based input‐constrained H ∞ control of nonlinear systems was presented based on adaptive critic designs and neural network implementation, and then Wang et al improved the adaptive critic technique by incorporating an improved critic learning criterion. In addition, Wang et al adopted a mixed data and event‐driven design approach to improve the adaptive critic learning technique. Moreover, an off‐policy reinforcement leaning method was introduced in the work of Luo et al to learn the solution of the HJI equation for nonlinear systems with unknown internal system model from real system data rather than the mathematical model.…”