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Event-driven H∞ control with critic learning for nonlinear systems.

Xiong Yang1, Zhongke Gao1, Jinhui Zhang2

  • 1School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China.

Neural Networks : the Official Journal of the International Neural Network Society
|August 30, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces an event-driven H∞ control method for nonlinear systems, converting it into a zero-sum game. The approach uses a novel triggering condition and adaptive critics for stability, validated with a pendulum system.

Keywords:
Adaptive critic designsCritic learningEvent-driven controlNeural network controlReinforcement learning

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Area of Science:

  • Control Theory
  • Nonlinear Systems
  • Game Theory

Background:

  • H∞ control is crucial for robust system performance.
  • Event-driven control offers efficiency but faces challenges like Zeno behavior.
  • Nonlinear systems require advanced control strategies.

Purpose of the Study:

  • To develop an event-driven H∞ control strategy for continuous-time nonlinear systems.
  • To address Zeno behavior in event-triggered control systems.
  • To propose a novel method for solving the event-driven Hamilton-Jacobi-Isaacs equation.

Main Methods:

  • Conversion of the nonlinear H∞ control problem into an event-driven two-player zero-sum game using a discounted cost function.
  • Development of an event-driven Hamilton-Jacobi-Isaacs equation (HJIE).
  • Proposal of a novel event-triggering condition to prevent Zeno behavior.
  • Utilization of an adaptive critic architecture with a unique critic neural network (NN) for solving the HJIE.
  • Stability analysis of the hybrid closed-loop system using Lyapunov's direct approach.

Main Results:

  • A novel event-triggering condition is proposed, ensuring no Zeno behavior.
  • The triggering threshold can remain positive without strict disturbance attenuation level selection.
  • An adaptive critic architecture effectively solves the event-driven HJIE.
  • Stability of the hybrid closed-loop system is rigorously analyzed.
  • The proposed event-driven H∞ control scheme is validated on nonlinear plants, including a pendulum system.

Conclusions:

  • The proposed event-driven H∞ control scheme is effective for continuous-time nonlinear systems.
  • The novel event-triggering condition enhances control system reliability by preventing Zeno behavior.
  • The adaptive critic approach provides a viable solution for complex control problems.