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Pinning impulsive control algorithms for complex network.

Wen Sun1, Jinhu Lü2, Shihua Chen3

  • 1School of Information and Mathematics, Yangtze University, Jingzhou 434023, People's Republic of China.

Chaos (Woodbury, N.Y.)
|April 5, 2014
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Summary
This summary is machine-generated.

This study introduces novel impulsive pinning control algorithms for complex dynamical networks. These methods enhance efficiency and reduce costs by controlling nodes at discrete times, applicable to both strongly and non-strongly connected networks.

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Area of Science:

  • Complex dynamical networks
  • Control theory
  • Network synchronization

Background:

  • Network synchronization is crucial for understanding complex systems.
  • Existing control methods can be communication-intensive and costly.
  • Impulsive control offers a potential for more efficient network management.

Purpose of the Study:

  • To develop and validate novel impulsive pinning control algorithms for complex dynamical networks.
  • To investigate the application of these algorithms to both strongly and non-strongly connected networks.
  • To enhance communication efficiency and reduce control costs in network synchronization.

Main Methods:

  • Design of two classes of pinning control algorithms utilizing impulsive signals.
  • Analysis of network synchronization for strongly connected networks.
  • Determination of pinning node requirements for non-strongly connected networks using Frobenius normal form.
  • Validation through illustrative examples.

Main Results:

  • A single controller can synchronize strongly connected networks with suitable coupling.
  • The Frobenius normal form dictates pinning strategy for non-strongly connected networks.
  • The proposed impulsive control is effective for various network structures, including asymmetric and irreducible coupling matrices.

Conclusions:

  • Impulsive pinning control offers an efficient and cost-effective approach to network synchronization.
  • The developed algorithms are robust and adaptable to different network topologies.
  • This work provides a theoretical and practical framework for controlling complex dynamical networks.