Output feedback stabilizer design of Boolean networks based on network structure

• Published in: Frontiers of information technology & electronic engineering Vol. 21; no. 2; pp. 247 - 259
• Main Authors: Zhong, Jie, Li, Bo-wen, Liu, Yang, Gui, Wei-hua
• Format: Journal Article
• Language: English
• Published: Hangzhou Zhejiang University Press 01.02.2020; Springer Nature B.V; School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China%School of Automation, Central South University, Changsha 410083, China; College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China%School of Information Science and Engineering, Southeast University, Nanjing 210096, China
• Subjects: Boolean; Boolean functions; Cell death; Communications Engineering; Computer Hardware; Computer Science; Computer Systems Organization and Communication Networks; Electrical Engineering; Electronics and Microelectronics; Instrumentation; Networks; Nodes; Output feedback; Pinning; Signal transduction; Stabilization; Tensors; Network structure; TP183; Output feedback stabilizer; Semi-tensor product of matrices; Boolean networks
• ISSN: 2095-9184; 2095-9230
• DOI: 10.1631/FITEE.1900229

In genetic regulatory networks, a stable configuration can represent the evolutionary behavior of cell death or unregulated growth in genes. We present analytical investigations on output feedback stabilizer design of Boolean networks (BNs) to achieve global stabilization via the semi-tensor product method. Based on network structure information describing coupling connections among nodes, an output feedback stabilizer is designed to achieve global stabilization. Compared with the traditional pinning control design, the output feedback stabilizer design is not based on the state transition matrix of BNs, which can efficiently determine pinning control nodes and reduce computational complexity. Our proposed method is efficient in that the calculation of the state transition matrix with dimension 2 n × 2 n is avoided; here n is the number of nodes in a BN. Finally, a signal transduction network and a D. melanogaster segmentation polarity gene network are presented to show the efficiency of the proposed method. Results are shown to be simple and concise, compared with traditional pinning control for BNs.