Categorization Problem on Controllability of Boolean Control Networks

• 成果类型: Article
• 署名作者: Zhu, Qunxi; Gao, Zuguang; Liu, Yang; Gui, Weihua
• 署名单位: Fudan University; University of Chicago; Zhejiang Normal University; Central South University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3002509
• 发表日期: 2021
• 页码: 2297-2303
• 关键词: Controllability; Biological systems; Biological system modeling; graph theory; tools; dynamical systems; Algebraic graph theory; Boolean control network (BCN); categorization; CONTROLLABILITY; semitensor product of matrices

摘要

A Boolean control network (BCN) is a discrete-time dynamical system whose variables take values from a binary set {0, 1}. At each time step, each variable of the BCN updates its value simultaneously according to a Boolean function which takes the state and control of the previous time step as its input. Given an ordered pair of states of a BCN, we define the set of reachable time steps as the set of positive integer k's where there exists a control sequence such that the BCN can be steered from one state to the other in exactly k time steps; and the set of unreachable time steps as the set of k's where there does not exist any control sequence such that the BCN can be steered from one state to the other in exactly k time steps. We consider in this article the so-called categorization problem of a BCN, i.e., we develop a method, via algebraic graph theoretic approach, to determine whether the set of reachable time steps and the set of unreachable time steps, associated with the given pair of states, are finite or infinite. Our results can be applied to classify all ordered pairs of states into four categories, depending on whether the set of reachable (unreachable) time steps is finite or not.