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Semi-global cluster synchronization for nonlinear systems under fixed and switching topologies.

Lu Ren1, Man Li2, Jian Liu3

  • 1School of Artificial Intelligence, Anhui University, Anhui 230601, China.

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|May 17, 2021
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Summary

This study addresses cluster synchronization in nonlinear systems with input saturation, developing controllers for fixed and switching network topologies. The research provides conditions for achieving synchronization, even with limited control input.

Keywords:
Input saturationNonlinear systemsSemi-global cluster synchronizationSwitching topology

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Network Science

Background:

  • Cluster synchronization is crucial for coordinated behavior in complex systems.
  • Input saturation in control systems presents significant challenges for achieving synchronization.
  • Heterogeneous systems and dynamic network topologies (switching) add complexity to synchronization problems.

Purpose of the Study:

  • To investigate cluster synchronization for heterogeneous nonlinear systems with input saturation.
  • To design distributed feedback controllers capable of handling input saturation.
  • To analyze synchronization under both fixed and switching network topologies.

Main Methods:

  • Utilized algebraic graph theory and Lyapunov methods for stability analysis.
  • Employed a low-gain feedback control technique to manage input saturation.
  • Developed synchronization protocols applicable to fixed and switching topologies.

Main Results:

  • Derived sufficient conditions for semi-global cluster synchronization.
  • Demonstrated the effectiveness of proposed protocols for both fixed and switching topologies.
  • Specified the lower bound for total activation time under switching topologies with directed spanning trees.

Conclusions:

  • The proposed distributed controllers effectively achieve semi-global cluster synchronization in heterogeneous nonlinear systems with input saturation.
  • The methods are validated for both static and dynamic (switching) network configurations.
  • The study contributes theoretical frameworks and practical protocols for complex system synchronization.