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Optimal synchronization with L2-gain performance: An adaptive dynamic programming approach.

Zitao Chen1, Kairui Chen2, Ruizhi Tang2

  • 1School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou, 510006, Guangdong, China; School of Mathematics, Southeast University, Nanjing, 211189, China; Department of Mathematical Sciences, Seoul National University, Seoul, 08826, Republic of Korea.

Neural Networks : the Official Journal of the International Neural Network Society
|August 1, 2024
PubMed
Summary
This summary is machine-generated.

This study presents an optimal control protocol for nonlinear multi-agent systems with unknown dynamics. The developed method ensures system stability and achieves Nash equilibrium for robust control.

Keywords:
-gain performanceAdaptive dynamic programmingMulti-agent systemNash equilibriumNeural network

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Area of Science:

  • Control Theory
  • Nonlinear Systems
  • Multi-Agent Systems

Background:

  • Designing optimal synchronous control for nonlinear multi-agent systems is challenging due to partially known dynamics and external disturbances.
  • The Hamilton-Jacobi-Isaacs (HJI) equation provides a framework for solving such optimal control problems.

Purpose of the Study:

  • To develop an optimal synchronous control protocol for nonlinear multi-agent systems.
  • To address challenges posed by partially known dynamics and uncertain external disturbances.
  • To achieve robust performance and stability.

Main Methods:

  • Derivation of the Hamilton-Jacobi-Isaacs equation using a performance index function and system dynamics.
  • Application of distributed policy iteration adaptive dynamic programming (ADP) for numerical solutions to the HJI equation.
  • Design of a neural network-based implementation for the control protocol.

Main Results:

  • Convergence of iterative variables to the HJI equation solution is proven.
  • L2-gain performance of the closed-loop system is achieved, ensuring stability.
  • The derived control protocol is demonstrated to be a Nash equilibrium solution.

Conclusions:

  • The proposed distributed ADP algorithm effectively solves the optimal control problem for nonlinear multi-agent systems.
  • The method guarantees system stability and optimal performance under uncertainty.
  • Neural network implementation provides a practical approach for real-world applications.