文献类型：期刊文献

英文题名：ON CONTROLLABILITY OF DELAYED BOOLEAN CONTROL NETWORKS

作者：Lu, Jianquan[1];Zhong, Jie[1];Ho, Daniel W. C.[2];Tang, Yang[3];Cao, Jinde[1]

机构：[1]Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China;[2]City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China;[3]E China Univ Sci & Technol, Minist Educ, Key Lab Adv Control & Optimizat Chem Proc, Shanghai 200237, Peoples R China

年份：2016

卷号：54

期号：2

起止页码：475

外文期刊名：SIAM JOURNAL ON CONTROL AND OPTIMIZATION

收录：;EI(收录号：20161902352927);WOS:【SCI-EXPANDED(收录号:WOS:000375552500003)】；

基金：The authors acknowledge the National Natural Science Foundation of China under grants 61175119, 61272530, 61590923, 61573102, and 61573096, and RGC of HKSAR under grant GRF CityU 11204514.

语种：英文

外文关键词：Boolean control networks; complex networks; time delay; controllability

摘要：This paper is devoted to studying the trajectory and state controllability of Boolean control networks (BCNs) with time delay. In contrast to BCNs without time delay, the dynamics of delayed BCNs are determined by a sequence of initial states, named here trajectories. Trajectory controllability means that there exists a control signal steering a system from an initial trajectory to a desired trajectory, while state controllability means that there exists a control signal steering an initial state to a given state. Here, both trajectory controllability and state controllability will be studied. It should be noted that in this paper, trajectory controllability does not mean tracking or following a given trajectory. In fact it means to control BCNs to a destination trajectory of length mu at the k-th step. Using the semi-tensor product of matrices, the delayed BCNs are first converted into an equivalent algebraic description, and then some necessary and sufficient conditions are derived for the trajectory controllability of delayed BCNs. We further present a bijection between the state of BCNs and the trajectory of length mu, which is then used to derive some necessary and sufficient conditions for the state controllability of delayed BCNs. Both the problems of controlling an initial state sequence to a desired state and a desired trajectory are first investigated. We also consider the issues of avoiding some specific states which may cause diseases or lead to dangerous situations. Numerical examples are given to illustrate our theoretical results.