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Adaptive dynamic programming for containment control with robustness analysis to iterative error: A global Nash

Zitao Chen1, Kairui Chen2, Jianhui Wang2

  • 1School of Mathematics, Southeast University, Nanjing, 211189, Jiangsu, PR China; School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou, 510006, Guangdong, PR China.

ISA Transactions
|September 11, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces an iterative algorithm to find the optimal containment control solution using graphical games. It ensures robustness against iterative errors, even without system dynamics knowledge.

Keywords:
Adaptive dynamic programmingContainment controlGlobal Nash equilibriumMulti-agent system

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Area of Science:

  • Control Theory
  • Game Theory
  • Optimization

Background:

  • Optimal containment control is crucial for multi-agent systems.
  • Global Nash equilibrium provides optimal solutions in graphical games.
  • Existing methods often lack robustness or require system dynamics knowledge.

Purpose of the Study:

  • To develop an iterative adaptive dynamic programming algorithm for solving the optimal containment control problem.
  • To analyze the robustness of the proposed algorithm against iterative errors.
  • To decouple Hamilton-Jacobi equations for guaranteed solvability of the global Nash equilibrium.

Main Methods:

  • Formulating the containment control problem as a graphical game.
  • Applying iterative adaptive dynamic programming.
  • Deriving sufficient conditions to decouple Hamilton-Jacobi equations.
  • Analyzing robustness to iterative errors.

Main Results:

  • A novel iterative algorithm for global Nash equilibrium in containment control.
  • Guaranteed solvability of the global Nash equilibrium solution.
  • Robustness analysis quantifying the impact of iterative errors.
  • Separation of control gain and coupling strength design procedures.

Conclusions:

  • The proposed algorithm effectively solves the optimal containment control problem.
  • The method is robust to iterative errors and does not require system dynamics.
  • The approach offers advantages over existing methods by avoiding trivial design cases.