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Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update.

Chao Luo1, Xingyuan Wang2, Hong Liu1

  • 11] School of Information Science and Engineering, Shandong Normal University, Jinan 250014, China [2] Shandong Provincial Key Laboratory for Novel Distributed Computer Software Technology, Jinan 250014, China.

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|December 18, 2014
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Summary
This summary is machine-generated.

This study investigates the controllability of asynchronous Boolean multiplex control networks with time delays. We developed a method to precisely control network states and determine the maximum probability of reaching a target state.

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Area of Science:

  • Control theory
  • Network science
  • Discrete dynamical systems

Background:

  • Asynchronous Boolean multiplex control networks (ABMCNs) are complex systems with applications in various fields.
  • Understanding their controllability under asynchronous updates and time delays is crucial for effective system design.
  • Existing models often simplify network dynamics, neglecting asynchronous behavior and time delays.

Purpose of the Study:

  • To analyze the controllability of ABMCNs with asynchronous updates and time delays.
  • To develop a mathematical framework for predicting and controlling the behavior of these networks.
  • To provide methods for steering the network to a desired state with maximum probability.

Main Methods:

  • Construction of a dynamical model for ABMCNs incorporating asynchronous updates and time delays.
  • Application of the semi-tensor product (STP) approach to convert logical dynamics into an algebraic form.
  • Derivation of control-depending network transition matrices for the delayed system.

Main Results:

  • A necessary and sufficient condition for controlling fixed points of the dynamics was established.
  • Formulas were derived to calculate reachable sets under specified and arbitrary controls at a given time.
  • Reachable probabilities to different destination states were determined, along with a method to find optimal control sequences.

Conclusions:

  • The proposed semi-tensor product approach effectively addresses the controllability of asynchronous Boolean multiplex control networks with time delays.
  • The derived conditions and formulas provide a robust framework for analyzing and controlling these complex systems.
  • The study offers practical methods for steering networks to target states with high probability, validated by illustrative examples.