Controllability of Conjunctive Boolean Networks with Application to Gene Regulation

Zuguang Gao, Xudong Chen, Tamer Basar

Research output: Contribution to journalArticlepeer-review


A Boolean network is a finite-state discrete-time dynamical system. At each step, each variable takes a value from a binary set. The value update rule for each variable is a local function which depends only on a selected subset of variables. Boolean networks have been used in modeling gene regulatory networks. In this paper, we focus on a special class of Boolean networks, namely, the conjunctive Boolean networks (CBNs), whose value update rule is comprised of only logic AND operations. It is known that any trajectory of a Boolean network will enter a periodic orbit. Periodic orbits of a CBN have been completely understood. In this paper, we investigate the orbit-controllability and state-controllability of a CBN: We ask the question of how one can steer a CBN to enter any periodic orbit or to reach any final state, from any initial state. We establish necessary and sufficient conditions for a CBN to be orbit-controllable and state-controllable. Furthermore, explicit control laws are presented along the analysis.

Original languageEnglish (US)
Pages (from-to)770-781
Number of pages12
JournalIEEE Transactions on Control of Network Systems
Issue number2
StatePublished - Jun 2018


  • Biological control systems
  • Boolean networks
  • controllability of discrete systems
  • networked control systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Control and Optimization


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