概率布尔网络的牵制鲁棒镇定

Pinning Robust Stabilization of Probabilistic Boolean Networks

文章研究概率布尔网络通过牵制控制器依概率1实现鲁棒镇定的问题.首先,利用矩阵的半张量积,给出带有干扰的概率布尔网络在牵制控制下的代数表示,通过牵制反馈控制器,改变了状态概率转移矩阵的列,得到了可在任意干扰下依概率1实现鲁棒镇定的概率布尔网络.其次,根据状态概率转移矩阵列的变化,确定牵制节点集,验证了牵制反馈矩阵的可解性并提出牵制控制器的设计算法.最后,给出实例说明结果的有效性.

In this paper,the problem of probabilistic Boolean networks which achieve robust stabilization with probability 1 under pinning control is studied.Firstly,by using semi-tensor product of matrices,the algebraic expression of probabilistic Boolean networks with interference is proposed under pinning control.By pinning state-feedback controllers,the columns of the state probability transition matrices are changed,and a new probabilistic Boolean network which can achieve robust stabilization with probability 1 is obtained under any interference.Secondly,the pinning nodes set is determined according to the change of the state probability transition matrices.In addition,the solvability of the pinning state-feedback matrices is verified and an algorithm for designing pinning controllers is proposed.Finally,an example is given to illustrate the effectiveness of the results.