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Neural network-based adaptive decentralized safe control for interconnected nonlinear systems with time delays.

Chong Liu1, Leiming Wang2, Zhousheng Chu2

  • 1College of Information and Control Engineering, Xi'an University of Architecture and Technology, Xi'an, 710055, Shaanxi, PR China; School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798, Singapore.

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Summary

This study introduces a decentralized dynamic event-triggered controller using adaptive dynamic programming for nonlinear systems with time delays and input constraints. The method ensures system stability and efficient control, even with non-zero equilibrium points.

Keywords:
Adaptive dynamic programming (ADP)Dynamic event-triggered (DET)Interconnected nonlinear systemsNeural network (NN)Safe controlTime delays

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Artificial Intelligence

Background:

  • Interconnected nonlinear systems with time delays and asymmetric input constraints present significant safety control challenges.
  • Existing control methods often assume zero equilibrium points, limiting their applicability to broader system dynamics.
  • Decentralized control strategies are crucial for managing large-scale interconnected systems efficiently.

Purpose of the Study:

  • To develop a decentralized dynamic event-triggered (DET) controller for interconnected nonlinear systems with non-zero equilibrium points, time delays, and asymmetric input constraints.
  • To transform a constrained control problem into an unconstrained optimal control problem (OCP) using a cost function incorporating a discount factor, barrier function, and Lyapunov-Krasovskii (L-K) function.
  • To address computational efficiency and the need for continuous excitation in adaptive dynamic programming (ADP) based control.

Main Methods:

  • A novel cost function is constructed for systems with non-zero equilibrium points, time delays, and constraints.
  • An event-based Hamilton-Jacobi-Bellman (HJB) equation is formulated and solved using ADP.
  • A decentralized dynamic event-triggered (DET) mechanism is proposed for enhanced computational efficiency.
  • Neural network (NN) weights are optimized via gradient descent and experience replay (ER) techniques, eliminating the need for continuous system excitation.

Main Results:

  • The proposed DET controller effectively handles interconnected nonlinear systems with non-zero equilibrium points, time delays, and asymmetric input constraints.
  • The adaptive dynamic programming approach, combined with ER, ensures efficient learning and control.
  • Theoretical analysis confirms the uniform ultimate boundedness (UUB) of system states and NN weights, while also excluding Zeno behavior.
  • The method's efficacy is demonstrated through a practical spring-pendulum system example.

Conclusions:

  • The developed decentralized dynamic event-triggered adaptive dynamic programming controller offers a robust and efficient solution for complex nonlinear systems.
  • The approach successfully addresses challenges related to non-zero equilibrium points, time delays, and input constraints.
  • The findings contribute to advancing safety control methodologies for large-scale interconnected systems.