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Formation deployment control of multi-agent systems modeled with PDE.

Sai Zhang1, Li Tang1, Yan-Jun Liu1

  • 1College of Science, Liaoning University of Technology, Jinzhou 121001, China.

Mathematical Biosciences and Engineering : MBE
|January 19, 2023
PubMed
Summary

This study presents a novel distributed cooperative control protocol for partial differential equation-based multi-agent systems (MASs). The proposed method enables MASs to achieve desired formations effectively, validated by theoretical analysis and simulations.

Keywords:
PDE-backsteppingformation controlleader-followermulti-agent systemswave PDE

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Area of Science:

  • Control Theory
  • Applied Mathematics
  • Robotics

Background:

  • Formation control is crucial for multi-agent systems (MASs).
  • Partial differential equation (PDE)-based MASs present unique control challenges.
  • Existing methods may lack distributed control or scalability.

Purpose of the Study:

  • To develop a distributed cooperative control protocol for PDE-based MASs.
  • To ensure stable formation control using a novel boundary control scheme.
  • To enable follower agents to achieve desired formations with local information.

Main Methods:

  • Development of MASs on a 1D chain topology using polar coordinates.
  • Simulation of MAS dynamics with a spatial-varying coefficient wave equation.
  • Proposal of a boundary control scheme combining PDE-backstepping and Volterra integral transformation.
  • Proof of kernel function well-posedness via iterative and inductive methods.
  • Stability analysis of the closed-loop system using Lyapunov direct method.
  • Discretization of the PDE model using the finite difference method.

Main Results:

  • A distributed cooperative control protocol was derived.
  • Follower agents require only local position information (self and neighbors).
  • The control protocol effectively drives MASs into desired formations.
  • Theoretical proofs confirm the well-posedness and stability of the control scheme.

Conclusions:

  • The proposed control scheme is effective for PDE-based MAS formation control.
  • The distributed nature of the protocol enhances scalability and practicality.
  • Numerical simulations validate the theoretical findings and control performance.