Event-Triggered Control for the Stabilization of Probabilistic Boolean Control Networks

Shiyong Zhu,Yuanyuan Li,Jungang Lou,Zhen Wang,Yang Liu

doi:10.1155/2018/9259348

Abstract

This paper realizes global stabilization for probabilistic Boolean control networks (PBCNs) with event-triggered state feedback control (ETSFC). Via the semitensor product (STP) of matrices, PBCNs with ETSFC are converted into discrete-time algebraic systems, based on which a necessary and sufficient condition is derived for global stabilization of PBCNs. Furthermore, an algorithm is presented to design a class of feasible event-triggered state feedback controllers for global stabilization. Finally, an illustrative example shows the effectiveness of the obtained result.

Highlights

As a central focus of genomic research, the way cellular systems fail in diseases has attracted much attention [1, 2]
(i) A series of reachability sets are defined, via which, a necessary and sufficient condition for global stabilization of probabilistic Boolean control networks (PBCNs) controlled by event-triggered state feedback control (ETSFC) is designed
(ii) An algorithm is presented to design a class of eventtriggered state feedback controllers to realize global stabilization of PBCNs

Summary

Introduction

As a central focus of genomic research, the way cellular systems fail in diseases has attracted much attention [1, 2]. A new matrix product, named the semitensor product (STP), is presented by Cheng et al [7] It converts the logical form of BCNs into the algebraic state space representation (ASSR). [18] first presented two kinds of event-trigger controllers to study the disturbance decoupling problems of BCNs, and some necessary and sufficient conditions were obtained. (i) A series of reachability sets are defined, via which, a necessary and sufficient condition for global stabilization of PBCNs controlled by ETSFC is designed. (ii) An algorithm is presented to design a class of eventtriggered state feedback controllers to realize global stabilization of PBCNs. The remaining part of this paper is constructed as follows.

Preliminaries

Main Results

Conclusion