On controllability and stabilizability of probabilistic Boolean control networks  

作　　者：ZHAO Yin CHENG DaiZhan 

机构地区：[1]Institute of Systems Science, Chinese Academy of Sciences

出　　处：《Science China(Information Sciences)》2014年第1期174-187,共14页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61074114,60821091)

摘　　要：The controllability of probabilistic Boolean control networks（PBCNs） is first considered. Using the input-state incidence matrices of all models, we propose a reachability matrix to characterize the joint reachability. Then we prove that the joint reachability and the controllability of PBCNs are equivalent, which leads to a necessary and sufcient condition of the controllability. Then, the result of controllability is used to investigate the stability of probabilistic Boolean networks（PBNs） and the stabilization of PBCNs. A necessary and sufcient condition for the stability of PBNs is obtained first. By introducing the control-fixed point of Boolean control networks（BCNs）, the stability condition has finally been developed into a necessary and sufcient condition of the stabilization of PBCNs. Both necessary and sufcient conditions for controllability and stabilizability are based on reachability matrix, which are easily computable. Hence the two necessary and sufcient conditions are straightforward verifiable. Numerical examples are provided from case to case to demonstrate the corresponding theoretical results.The controllability of probabilistic Boolean control networks（PBCNs） is first considered. Using the input-state incidence matrices of all models, we propose a reachability matrix to characterize the joint reachability. Then we prove that the joint reachability and the controllability of PBCNs are equivalent, which leads to a necessary and sufcient condition of the controllability. Then, the result of controllability is used to investigate the stability of probabilistic Boolean networks（PBNs） and the stabilization of PBCNs. A necessary and sufcient condition for the stability of PBNs is obtained first. By introducing the control-fixed point of Boolean control networks（BCNs）, the stability condition has finally been developed into a necessary and sufcient condition of the stabilization of PBCNs. Both necessary and sufcient conditions for controllability and stabilizability are based on reachability matrix, which are easily computable. Hence the two necessary and sufcient conditions are straightforward verifiable. Numerical examples are provided from case to case to demonstrate the corresponding theoretical results.

关 键 词：probabilistic Boolean control network CONTROLLABILITY STABILITY STABILIZATION semi-tensor product 

分 类 号：O157.5[理学—数学] O231[理学—基础数学]