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Controllability of asynchronous Boolean multiplex control networks.

Chao Luo1, Xingyuan Wang2, Hong Liu1

  • 1School of Information Science and Engineering, Shandong Normal University, Jinan 250014, China.

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Summary
This summary is machine-generated.

This study investigates the controllability of asynchronous Boolean multiplex control networks (ABMCNs). Researchers developed methods to determine system reachability and control probabilities, offering insights into network state transitions.

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Area of Science:

  • Control Theory
  • Network Science
  • Discrete Mathematics

Background:

  • Asynchronous Boolean multiplex control networks (ABMCNs) are complex systems with applications in various fields.
  • Understanding the controllability of these networks is crucial for designing and managing them effectively.
  • Existing models often lack comprehensive methods for analyzing asynchronous update mechanisms.

Purpose of the Study:

  • To present a model for ABMCNs under asynchronous updates.
  • To develop a framework for analyzing the controllability of ABMCNs.
  • To provide methods for calculating reachable states and control probabilities.

Main Methods:

  • Utilizing the semi-tensor product approach to convert logical dynamics into linear representation.
  • Deriving generalized formulas for control-dependent network transition matrices.
  • Proposing a necessary and sufficient condition for controlling fixed points with probability one.

Main Results:

  • A generalized formula for control-dependent network transition matrices was achieved.
  • A condition was established to verify the one-probability control of fixed points in ABMCNs.
  • Formulas were derived for reachable sets at time 's' under specified and arbitrary controls, and for state transition probabilities.

Conclusions:

  • The study provides a robust framework for analyzing the controllability of ABMCNs.
  • An algorithm for calculating overall reachable states and an approach for finding optimal control sequences were presented.
  • The proposed methods are validated through illustrative examples, demonstrating their practical feasibility.