Sampled-Data Stabilization for Boolean Control Networks With Infinite Stochastic Sampling

Sampled-data state feedback control with stochastic sampling periods for Boolean control networks (BCNs) is investigated in this article. First, based on the algebraic form of BCNs, stochastic sampled-data state feedback control is applied to stabilize the considered system to a fixed point or a giv...

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Published inIEEE transactions on cybernetics Vol. 52; no. 1; pp. 333 - 343
Main Authors Wang, Liqing, Wu, Zheng-Guang, Chen, Shiming
Format Journal Article
LanguageEnglish
Published United States IEEE 01.01.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Asymptotic stability
Boolean
Boolean algebra
Boolean network (BN)
Control systems
Feedback
Feedback control
Fourier transforms
infinite stochastic sampling periods
Linear programming
Markov Chains
Markov processes
Neural Networks, Computer
Sampling
semitensor product (STP)
set stabilization
Stability analysis
Stabilization
State feedback
Switches
Online AccessGet full text
ISSN2168-2267
2168-2275
2168-2275
DOI10.1109/TCYB.2019.2962389

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Abstract Sampled-data state feedback control with stochastic sampling periods for Boolean control networks (BCNs) is investigated in this article. First, based on the algebraic form of BCNs, stochastic sampled-data state feedback control is applied to stabilize the considered system to a fixed point or a given set. Two kinds of distributions of stochastic sampling periods are considered. First, the distribution of sampling periods is assumed to be independent identically distributed (i.i.d.) in the range of any positive integers and the second distribution of sampling periods is assumed to follow an infinite Markov process. A BCN with infinite stochastic sampling periods proves to be equivalent to a finite stochastic switched system, based on which, necessary and sufficient conditions are given to guarantee the stabilization and set stabilization of the BCN with stochastic sampling periods. For the first one, two algorithms are given to guarantee the stabilization and set stabilization of the considered system. For the second one, necessary and sufficient conditions are all presented in the linear programming form. Examples are listed to show the effectiveness of our results.
AbstractList Sampled-data state feedback control with stochastic sampling periods for Boolean control networks (BCNs) is investigated in this article. First, based on the algebraic form of BCNs, stochastic sampled-data state feedback control is applied to stabilize the considered system to a fixed point or a given set. Two kinds of distributions of stochastic sampling periods are considered. First, the distribution of sampling periods is assumed to be independent identically distributed (i.i.d.) in the range of any positive integers and the second distribution of sampling periods is assumed to follow an infinite Markov process. A BCN with infinite stochastic sampling periods proves to be equivalent to a finite stochastic switched system, based on which, necessary and sufficient conditions are given to guarantee the stabilization and set stabilization of the BCN with stochastic sampling periods. For the first one, two algorithms are given to guarantee the stabilization and set stabilization of the considered system. For the second one, necessary and sufficient conditions are all presented in the linear programming form. Examples are listed to show the effectiveness of our results.Sampled-data state feedback control with stochastic sampling periods for Boolean control networks (BCNs) is investigated in this article. First, based on the algebraic form of BCNs, stochastic sampled-data state feedback control is applied to stabilize the considered system to a fixed point or a given set. Two kinds of distributions of stochastic sampling periods are considered. First, the distribution of sampling periods is assumed to be independent identically distributed (i.i.d.) in the range of any positive integers and the second distribution of sampling periods is assumed to follow an infinite Markov process. A BCN with infinite stochastic sampling periods proves to be equivalent to a finite stochastic switched system, based on which, necessary and sufficient conditions are given to guarantee the stabilization and set stabilization of the BCN with stochastic sampling periods. For the first one, two algorithms are given to guarantee the stabilization and set stabilization of the considered system. For the second one, necessary and sufficient conditions are all presented in the linear programming form. Examples are listed to show the effectiveness of our results.
Sampled-data state feedback control with stochastic sampling periods for Boolean control networks (BCNs) is investigated in this article. First, based on the algebraic form of BCNs, stochastic sampled-data state feedback control is applied to stabilize the considered system to a fixed point or a given set. Two kinds of distributions of stochastic sampling periods are considered. First, the distribution of sampling periods is assumed to be independent identically distributed (i.i.d.) in the range of any positive integers and the second distribution of sampling periods is assumed to follow an infinite Markov process. A BCN with infinite stochastic sampling periods proves to be equivalent to a finite stochastic switched system, based on which, necessary and sufficient conditions are given to guarantee the stabilization and set stabilization of the BCN with stochastic sampling periods. For the first one, two algorithms are given to guarantee the stabilization and set stabilization of the considered system. For the second one, necessary and sufficient conditions are all presented in the linear programming form. Examples are listed to show the effectiveness of our results.
Author Chen, Shiming
Wu, Zheng-Guang
Wang, Liqing
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SubjectTerms Algorithms
Asymptotic stability
Boolean
Boolean algebra
Boolean network (BN)
Control systems
Feedback
Feedback control
Fourier transforms
infinite stochastic sampling periods
Linear programming
Markov Chains
Markov processes
Neural Networks, Computer
Sampling
semitensor product (STP)
set stabilization
Stability analysis
Stabilization
State feedback
Switches
Title Sampled-Data Stabilization for Boolean Control Networks With Infinite Stochastic Sampling
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