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Energy scaling and reduction in controlling complex networks.

Yu-Zhong Chen1, Le-Zhi Wang1, Wen-Xu Wang2

  • 1School of Electrical, Computer, and Energy Engineering, Arizona State University , Tempe, AZ 85287, USA.

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Controlling complex networks requires significant energy, following a scaling law. Identifying longest control chains (LCCs) offers a strategy to drastically reduce this energy, crucial for network control.

Keywords:
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Area of Science:

  • Network Science
  • Dynamical Systems Theory
  • Control Theory

Background:

  • Network control energy scales algebraically with the number of drivers.
  • Using minimal drivers (structural controllability) can lead to energy divergence.

Purpose of the Study:

  • To develop a physical theory explaining energy scaling in complex networks.
  • To identify fundamental structural elements governing control energy.
  • To propose a strategy for reducing network control energy.

Main Methods:

  • Identification of longest control chains (LCCs) as key structural elements.
  • Development of a physical theory linking LCCs to energy scaling.
  • Formulation of a control strategy based on LCCs.

Main Results:

  • The energy required for network control is dominated by longest control chains (LCCs).
  • A strategy based on LCCs can drastically reduce control energy in real-world networks.
  • Algebraic scaling laws govern energy distribution in complex network control.

Conclusions:

  • Longest control chains (LCCs) are fundamental to understanding and minimizing network control energy.
  • The LCC-based strategy offers significant energy reduction for controlling complex and nonlinear dynamical networks.
  • This work provides insights into energy efficiency for complex system control.