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Using In Vitro Fluorescence Resonance Energy Transfer to Study the Dynamics Of Protein Complexes at a Millisecond Time Scale
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Energy cost for controlling complex networks with linear dynamics.

Gaopeng Duan1,2, Aming Li3,4, Tao Meng1

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This study reveals the scaling behavior of minimum energy needed for complex network control. Our findings provide a precise upper bound, enabling cost-effective control of linear dynamical networks.

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Area of Science:

  • Network Science
  • Control Theory
  • Systems Engineering

Background:

  • Controllability of complex networks is a key research area.
  • Existing studies focus on steering systems and lower bounds of control energy.
  • Analytic expressions for the upper bound of minimum energy remain elusive.

Purpose of the Study:

  • To theoretically determine the scaling behavior of the upper bound of minimum energy for complex network control.
  • To derive more precise analytical results for the lower bound of minimum energy.
  • To enable cost-effective control of complex networks.

Main Methods:

  • Theoretical analysis to derive the scaling behavior of the minimum energy upper bound.
  • Numerical simulations to validate analytical findings.
  • Development of a method for deriving precise lower bound energy results.

Main Results:

  • A precise analytical expression for the upper bound of minimum energy is established.
  • The scaling behavior of this upper bound with respect to control time is determined.
  • More accurate analytical results for the lower bound of minimum energy are derived.

Conclusions:

  • The derived upper bound provides crucial insights into the minimum energy required for network control.
  • Findings are applicable to networks with multiple input nodes and linear dynamics.
  • This research facilitates practical implementation of minimum-cost control for complex networks.