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

• Published in: IEEE transactions on cybernetics Vol. 52; no. 1; pp. 333 - 343
• Main Authors: Wang, Liqing, Wu, Zheng-Guang, Chen, Shiming
• Format: Journal Article
• Language: English
• 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
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2019.2962389

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.