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).

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 -