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Optimal Asynchronous Stabilization for Boolean Control Networks With Lebesgue Sampling.

Liqing Wang, Zheng-Guang Wu

IEEE Transactions on Cybernetics

|October 15, 2020

Summary

This summary is machine-generated.

This study stabilizes Boolean control networks (BCNs) using semitensor products (STPs) and sampled-data state-feedback control (SDSFC) with Lebesgue sampling. It provides conditions for stabilization and designs control gains for optimal convergence.

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Area of Science:

Control Theory
Network Science
Discrete Mathematics

Background:

Boolean control networks (BCNs) are widely used to model complex biological and engineered systems.
Stabilizing BCNs to desired states is crucial for reliable system operation.
Existing control methods often face challenges with asynchronous or time-varying sampling.

Purpose of the Study:

To develop a novel sampled-data state-feedback control (SDSFC) strategy for stabilizing Boolean control networks (BCNs) using semitensor products (STPs).
To establish necessary and sufficient conditions for BCN stabilization under Lebesgue sampling regions.
To design asynchronous SDSFC gains and an algorithm for optimal control and fastest convergence.

Main Methods:

Application of semitensor products (STPs) of matrices to transform BCNs into equivalent switching systems.
Development of control strategies for single and multiple Lebesgue sampling regions (Sτ).
Design of asynchronous SDSFC gains based on reachable sets and optimization algorithms.

Main Results:

A necessary and sufficient condition for stabilizing BCNs with Lebesgue sampling regions is derived.
Asynchronous SDSFC gains are designed, enabling stabilization to fixed points.
An algorithm is presented to achieve minimal control times and fastest convergence rates.
The method is extended to multiple Lebesgue sampling regions and validated with examples, including a biological system.

Conclusions:

The proposed SDSFC with Lebesgue sampling effectively stabilizes BCNs, including stochastic variants.
The developed methods provide a robust framework for control design under time-varying sampling.
The results offer practical implications for controlling complex networks in various domains.