Orbit-controlling sets for conjunctive Boolean networks

Zuguang Gao, Xudong Chen, Tamer Başar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publication2017 American Control Conference, ACC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4989-4994
Number of pages6
ISBN (Electronic)9781509059928
DOIs
StatePublished - Jun 29 2017
Event2017 American Control Conference, ACC 2017 - Seattle, United States
Duration: May 24 2017May 26 2017

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2017 American Control Conference, ACC 2017
CountryUnited States
CitySeattle
Period5/24/175/26/17

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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