TY - GEN
T1 - Orbit-controlling sets for conjunctive Boolean networks
AU - Gao, Zuguang
AU - Chen, Xudong
AU - Başar, Tamer
N1 - Publisher Copyright:
© 2017 American Automatic Control Council (AACC).
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/6/29
Y1 - 2017/6/29
N2 - A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a local function, i.e., it depends only on a selected subset of variables. Boolean networks have been widely used in modeling gene regulatory networks. We focus in this paper on a special class of Boolean networks, termed as conjunctive Boolean networks. A Boolean network is called conjunctive if the associated value update rule is comprised of only AND operations. It is known that any trajectory of a finite dynamical system will enter into a periodic orbit. Periodic orbits of a conjunctive Boolean network have been completely understood. In this paper, we investigate the orbit-controllability of a conjunctive Boolean network: We ask the question of how one can steer the network from any initial state to a state in any periodic orbit. Specifically, we assume that there is a selected subset of variables in the network whose values are under control. We then establish a necessary and sufficient condition for the conjunctive Boolean network to be orbit-controllable. Furthermore, we present an explicit control law for steering the network from any initial condition to any periodic orbit.
AB - A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a local function, i.e., it depends only on a selected subset of variables. Boolean networks have been widely used in modeling gene regulatory networks. We focus in this paper on a special class of Boolean networks, termed as conjunctive Boolean networks. A Boolean network is called conjunctive if the associated value update rule is comprised of only AND operations. It is known that any trajectory of a finite dynamical system will enter into a periodic orbit. Periodic orbits of a conjunctive Boolean network have been completely understood. In this paper, we investigate the orbit-controllability of a conjunctive Boolean network: We ask the question of how one can steer the network from any initial state to a state in any periodic orbit. Specifically, we assume that there is a selected subset of variables in the network whose values are under control. We then establish a necessary and sufficient condition for the conjunctive Boolean network to be orbit-controllable. Furthermore, we present an explicit control law for steering the network from any initial condition to any periodic orbit.
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U2 - 10.23919/ACC.2017.7963728
DO - 10.23919/ACC.2017.7963728
M3 - Conference contribution
AN - SCOPUS:85010816298
T3 - Proceedings of the American Control Conference
SP - 4989
EP - 4994
BT - 2017 American Control Conference, ACC 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 American Control Conference, ACC 2017
Y2 - 24 May 2017 through 26 May 2017
ER -