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L0 norm constraint based external control source allocation for the minimum cost control of directed networks.

Lei Deng1, Guoqi Li2, Jing Pei2

  • 1Department of Precision Instrument, Center for Brain Inspired Computing Research, Tsinghua University, Beijing, 100084, China; Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA.

ISA Transactions
|March 18, 2018
PubMed
Summary

This study introduces a new method for finding key nodes in directed networks to minimize control costs. The L0-norm constraint based projected gradient method (LPGM) efficiently identifies optimal control nodes.

Keywords:
Directed networksKey nodes selectionL(0) normMinimum cost controlProbabilistic projection

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Area of Science:

  • Control Theory
  • Network Science
  • Applied Mathematics

Background:

  • The minimum cost control problem is crucial for managing directed networks.
  • Current methods for selecting key nodes connected to control sources can be inefficient for diverse networks.

Purpose of the Study:

  • To develop a novel, efficient iterative method for identifying key nodes in directed networks.
  • To address the limitations of existing techniques in the minimum cost control problem.

Main Methods:

  • Proposed an iterative method: L0-norm constraint based projected gradient method (LPGM).
  • Probabilistically searched the input matrix by constraining its L0 norm to a fixed value M.
  • Ensured each control source connects to a single key node throughout the search.

Main Results:

  • The LPGM efficiently converges to a suboptimal key node set within a few iterations.
  • Demonstrated improved performance over existing methods for selecting key nodes.

Conclusions:

  • The LPGM offers a new perspective for key node selection in directed network control.
  • This method provides an efficient solution for the minimum cost control problem.