title: Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update.
abstract: In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) with time delay is studied. Firstly, dynamical model of Boolean multiplex control networks is constructed, which is assumed to be under Harvey' asynchronous update and time delay is introduced both in states and controls. By using of semi-tensor product (STP) approach, the logical dynamics is converted into an equivalent algebraic form by obtaining the control-depending network transition matrices of delayed system. Secondly, a necessary and sufficient condition is proved that only control-depending fixed points of the studied dynamics can be controlled with probability one. Thirdly, respectively for two types of controls, the controllability of dynamical control system is investigated. When initial states and time delay are given, formulae are obtained to show a) the reachable set at time s under specified controls; b) the reachable set at time s under arbitrary controls; c) the reachable probabilities to different destination states. Furthermore, an approach is discussed to find a precise control sequence which can steer dynamical system into a specified target with the maximum reachable probability. Examples are shown to illustrate the feasibility of the proposed scheme.
authors.affiliation: 1] School of Information Science and Engineering, Shandong Normal University, Jinan 250014, China [2] Shandong Provincial Key Laboratory for Novel Distributed Computer Software Technology, Jinan 250014, China.
authors.forename: Chao
authors.initials: C
authors.lastname: Luo
authors.affiliation: Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China.
authors.forename: Xingyuan
authors.initials: X
authors.lastname: Wang
authors.affiliation: 1] School of Information Science and Engineering, Shandong Normal University, Jinan 250014, China [2] Shandong Provincial Key Laboratory for Novel Distributed Computer Software Technology, Jinan 250014, China.
authors.forename: Hong
authors.initials: H
authors.lastname: Liu