Recurrent output tracking of Boolean networks

• Published in: Nonlinear analysis. Hybrid systems Vol. 56; p. 101583
• Main Authors: Jiang, Chunfeng, Fu, Shihua, Del Vecchio, Carmen, Wang, Biao, Wang, Jianjun, Zhao, Jianli
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2025
• Subjects: Boolean control networks; Recurrent output tracking; Recurrent period; Semi-tensor product; State feedback control; State feedback control; Recurrent period; Semi-tensor product; Recurrent output tracking; Boolean control networks
• ISSN: 1751-570X
• DOI: 10.1016/j.nahs.2025.101583

This paper addresses the recurrent output tracking problem (ROTP) in Boolean networks (BNs), that is the property of systems output to intermittently and infinitely track a desired reference signal over long-term operation. Leveraging the semi-tensor product of matrices as the primary analytical tool, the study proposes solvability criteria for ROTP in both BNs and Boolean control networks (BCNs), and proposes algorithms to identify all states that enable recurrent tracking of the reference signal in these systems. Additionally, a truth matrix-based method is used to design state feedback controllers, ensuring ROTP solvability for BCNs initiating from such states. The study also explores the periodicity of the recurrent output tracking in B(C)Ns, demonstrating that the output tracking problem is a specific instance of the ROTP. The effectiveness of the proposed methods and results is validated through illustrative examples.