Improving the Critic Learning for Event-Based Nonlinear $H_{\infty }$ Control Design.

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Nonlinear Dynamics

Background:

• Event-based control offers advantages in reducing communication and computation.
• Nonlinear H∞ control is crucial for systems with uncertainties and disturbances.
• Adaptive critic mechanisms provide a powerful framework for optimal control design.

Purpose of the Study:

• To develop an improved critic learning criterion for event-based nonlinear H∞ state feedback control.
• To achieve minimax optimization for control and disturbance laws in an event-based setting.
• To eliminate the need for initial stabilizing control and avoid Zeno behavior.

Main Methods:

• Formulating the H∞ control problem as a two-player zero-sum game.
• Employing an adaptive critic mechanism with an improved updating rule.
• Training a single critic neural network to approximate optimal control and disturbance laws.
• Modeling the closed-loop system as an impulsive system and analyzing stability.
• Establishing a lower bound for the minimal intersample time to prevent Zeno behavior.

Main Results:

• An event-based optimal control law and a time-based worst-case disturbance law were obtained.
• The necessity of initial stabilizing control was removed.
• Stability of the closed-loop system was ensured through the improved learning criterion.
• Zeno behavior was successfully avoided.
• The method demonstrated efficient performance in simulations for aircraft and robot arm systems.

Conclusions:

• The proposed event-based nonlinear H∞ control design enhances critic learning for improved performance.
• The novel approach simplifies implementation by removing the need for initial stabilization.
• The method effectively addresses stability and Zeno behavior concerns in event-based control systems.