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Research Article | Open Access

Trajectory tracking approach to logical (control) networks

Xiaoyu Zhao1,2( ), Shihua Fu3,4
School of Mathematics, Shandong University, Jinan, Shandong 250100, China
Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao 266237, China
Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng University, Liaocheng 252000, China
School of Mathematical Science, Liaocheng University, Liaocheng 252000, China
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Abstract

Vector form expression of logical (control) networks is presented. From this aspect, the trajectory table is proposed to investigate Boolean networks. Based on it, the topology structure, controllability and observability of logical (control) networks are analyzed. Compared to the method of logical matrix, vector form expression called structure vector method decreases the computational complex. Numerical examples show that the complexity of the structure vector method is greatly reduced.

Keywords

semi-tensor product (STP) of matricesvector form expressionattractorscontrollability matrix
CLC number: 93-XX

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 9668-9682
DOI: 10.3934/math.2022538

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Cite this article:
Zhao X, Fu S. Trajectory tracking approach to logical (control) networks. AIMS Mathematics, 2022, 7(6): 9668-9682. https://doi.org/10.3934/math.2022538

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Received: 23 December 2021
Revised: 23 February 2022
Accepted: 01 March 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)