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Suboptimal distributed cooperative control for linear multi-agent system via Riccati design.

Shubo Li1, Tao Feng2, Jilie Zhang1

  • 1School of Information Science and Technology, Southwest Jiaotong University, China.

ISA Transactions
|December 14, 2024
PubMed
Summary

We developed a new control scheme for multi-agent systems (MAS) that optimizes performance using graph properties. This approach provides a guaranteed upper bound on system costs for both undirected and directed networks.

Keywords:
Directed graphDistributed controlMulti-agent systemRiccati designSuboptimal control

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Area of Science:

  • Control Theory
  • Networked Systems
  • Systems Engineering

Background:

  • Multi-agent systems (MAS) are crucial in various applications, requiring efficient distributed control strategies.
  • Existing cooperative control methods often face limitations in performance guarantees and applicability to different network topologies.

Purpose of the Study:

  • To propose a suboptimal distributed cooperative control scheme for continuous-time linear MAS.
  • To ensure a specified global quadratic cost functional is achieved over undirected and directed graphs.
  • To develop a control design method that is independent of the largest eigenvalue for undirected graphs.

Main Methods:

  • Derivation of the cost functional for a distributed linear feedback protocol in undirected graphs.
  • Solving a parametric algebraic Riccati equation (PARE) dependent on algebraic connectivity.
  • Extension of the method to directed graphs using row and column Laplacian matrices.

Main Results:

  • The cost functional is upper bounded by a quadratic form of the MAS's initial state.
  • A minimum upper bound is derived using PARE, depending solely on algebraic connectivity.
  • The proposed suboptimal distributed design method achieves a cost functional less than a specified positive scalar.
  • Effectiveness verified through numerical examples for both graph types.

Conclusions:

  • The proposed control scheme offers a robust and efficient method for MAS control.
  • The approach provides performance guarantees applicable to both undirected and directed network structures.
  • The method's independence from the largest eigenvalue offers an advantage over existing techniques for undirected graphs.