On detectability of Boolean control networks. (May 2020)

• Record Type: Journal Article
• Authors: Wang, Biao; Feng, Jun-e; Li, Haitao; Yu, Yongyuan
• Is Part Of: Nonlinear analysis. Volume 36(2020)
• Publication Date: 2020-05
• Subjects: Boolean control networks -- Detectability -- Observability -- Semi-tensor product; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2020.100859
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper introduces the detectability notions and investigates the detectability properties for Boolean networks (BNs) and Boolean control networks (BCNs). A BN (BCN) possesses the property of detectability if the current state can be determined by limited observed data. According to different situations, three types of detectabilities are defined: strong detectability, detectability and weak detectability. Firstly, using the semi-tensor product of matrices, the BCN is written as an equivalent algebraic expression, which is called the data form. Secondly, some criterion and detection algorithms are provided for checking detectabilities via this novel form. Thirdly, four types of properties: stability, stabilizability, observability and detectability, are compared and analyzed, and then their relationships are clearly described in two diagrams, which provide a new perspective to analyze the characterization of BNs and BCNs. Finally, for better presentation, two practical examples are presented to show the effectiveness of the obtained new results.