Paper Info
Title
On Controllability of Delayed Boolean Control Networks.
Abstract
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.
Year
DOI
Venue
2016
10.1137/140991820
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
Boolean control networks,complex networks,time delay,controllability
Mathematical optimization,Algebraic number,Existential quantification,Controllability,Matrix (mathematics),Control theory,Network controllability,Complex network,Trajectory,Mathematics
Journal
Volume
Issue
ISSN
54
2
0363-0129
Citations 
PageRank 
References 
46
1.10
22
Authors
5
Name
Order
Citations
PageRank
Jianquan Lu12337116.05
Jie Zhong217114.53
Daniel W.C. Ho35311285.38
Yang Tang439221.87
Jinde Cao511399733.03