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Sampled-Data State Feedback Stabilization of Boolean Control Networks.

Yang Liu1, Jinde Cao2, Liangjie Sun3

  • 1Department of Mathematics, Southeast University, Nanjing 210096, China, and College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China liuyang@zjnu.edu.cn.

Neural Computation
|February 19, 2016
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Summary
This summary is machine-generated.

This study explores sampled-data state feedback control (SDSFC) for Boolean control networks (BCNs). We establish conditions for global stabilization, showing SDSFC is equivalent to piecewise constant control (PCC).

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Area of Science:

  • Control Theory
  • Discrete Dynamical Systems
  • Computer Science

Background:

  • Boolean control networks (BCNs) are discrete models widely used in systems biology and computer science.
  • State feedback control is crucial for stabilizing BCNs, but sampled-data control introduces unique challenges.
  • Existing methods for BCN control often do not account for the discrete nature of sampled data.

Purpose of the Study:

  • To investigate the sampled-data state feedback control (SDSFC) problem for Boolean control networks (BCNs).
  • To derive necessary and sufficient conditions for the global stabilization of BCNs using SDSFC.
  • To explore the relationship between SDSFC and piecewise constant control (PCC) in BCNs.

Main Methods:

  • Utilizing the controllability matrix to derive conditions for stabilization.
  • Analyzing the behavior of BCN trajectories under piecewise constant control.
  • Developing algorithms for constructing sampled-data state feedback controllers.

Main Results:

  • Necessary and sufficient conditions for the global stabilization of BCNs via SDSFC were established.
  • New phenomena specific to SDSFC in BCNs were identified, differing from conventional state feedback.
  • The global stabilization of BCNs under SDSFC was proven to be equivalent to stabilization by PCC.

Conclusions:

  • Sampled-data state feedback control offers a viable method for stabilizing Boolean control networks.
  • The derived conditions and control construction algorithms provide practical tools for BCN analysis and design.
  • The equivalence between SDSFC and PCC simplifies the understanding and implementation of control strategies for BCNs.