Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control  

带状态反馈控制的概率布尔网络上基于互模拟的稳定性研究（英文）

作　　者：Nan JIANG Chi HUANG Yao CHEN Jürgen KURTHS 

机构地区：[1]School of Economic Information Engineering,Southwestern University of Finance and Economics,Chengdu 611130,China [2]School of Mathematics,Southeast University,Nanjing 210096,China [3]Potsdam Inslxtute for Climate Impact Research,Potsdam 14412,Germany [4]Department of Phystcs,Humboldt-Universitcit zu Berlin,Berlin 12489,Germany [5]Samtov State University,Saratov 410012,Russia

出　　处：《Frontiers of Information Technology & Electronic Engineering》2020年第2期268-280,共13页信息与电子工程前沿（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.61603268 and 61773319);the Fundamental Research Funds for the Central Universities,China(No.JBK190502)。

摘　　要：This study is concerned with probabilistic Boolean control networks(PBCNs)with state feedback control.A novel definition of bisimilar PBCNs is proposed to lower computational complexity.To understand more on bisimulation relations between PBCNs,we resort to a powerful matrix manipulation called semi-tensor product(STP).Because stabilization of networks is of critical importance,the propagation of stabilization with probability one between bisimilar PBCNs is then considered and proved to be attainable.Additionally,the transient periods(the maximum number of steps to implement stabilization)of two PBCNs are certified to be identical if these two networks are paired with a bisimulation relation.The results are then extended to the probabilistic Boolean networks.This study is concerned with probabilistic Boolean control networks(PBCNs) with state feedback control. A novel definition of bisimilar PBCNs is proposed to lower computational complexity. To understand more on bisimulation relations between PBCNs, we resort to a powerful matrix manipulation called semi-tensor product(STP). Because stabilization of networks is of critical importance, the propagation of stabilization with probability one between bisimilar PBCNs is then considered and proved to be attainable. Additionally, the transient periods(the maximum number of steps to implement stabilization) of two PBCNs are certified to be identical if these two networks are paired with a bisimulation relation. The results are then extended to the probabilistic Boolean networks.

关 键 词：PROBABILISTIC BOOLEAN CONTROL network BISIMULATION STABILIZATION with PROBABILITY one State feedback CONTROL 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]