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Ledley Solution Method for All Feasible State Feedback Stabilizers of Boolean Control Networks With Disturbances

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  • Control Theory and Applications
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Abstract

This paper addresses the robust stabilization problem of Boolean control networks with disturbance inputs (DBCNs) via the semi-tensor product (STP) of matrices, and designs all feasible state feedback stabilizers. Based on the algebraic form of DBCNs, some necessary and sufficient conditions are derived for the robust stabilization of DBCNs by Ledley antecedence solution technique. An algorithm is proposed to determine all complete families of robust reachable sets, moreover, all feasible state feedback stabilizers are obtained. Finally, two numerical examples are exploited to illustrate the effectiveness of the proposed results as well as the controller design scheme.

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Authors and Affiliations

  1. School of Mathematical Science, Liaocheng University, Liaocheng, 252026, China

    Xinling Li, Shihua Fu & Jianjun Wang

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  1. Xinling Li
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  2. Shihua Fu
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  3. Jianjun Wang
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Correspondence to Shihua Fu.

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This work is supported by the National Natural Science Foundation of China under grants 62103176, and the Natural Science Foundation of Shandong Province under grant ZR2019BF023.

Xinling Li received her Ph.D. degree from the School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, China, in 2020. She is currently with the School of Mathematical Science, Liaocheng University, Liaocheng, China. Her research interests include Boolean networks, game theory, and logical dynamic systems.

Shihua Fu received her Ph.D. degree from the School of Control Science and Engineering, Shandong University, Shandong, China, in 2018. Since 2018, she is a teacher with the School of Mathematical Sciences, Liaocheng University, Liaocheng, China. Her research interests include semi-tensor product of matrices, and its application in networked evolutionary games and logical networks.

Jianjun Wang received his B.S. and M.S. degrees from the School of Mathematical Sciences, Liaocheng University, Liaocheng, China, in 2015 and 2018, respectively. He received a Ph.D. degree from the School of Science and Technology, University of Camerino, Camerino, Italy, in 2022. His research interests include game theory and application, and logical dynamic systems.

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Li, X., Fu, S. & Wang, J. Ledley Solution Method for All Feasible State Feedback Stabilizers of Boolean Control Networks With Disturbances. Int. J. Control Autom. Syst. 22, 84–92 (2024). https://doi.org/10.1007/s12555-022-0590-x

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  • DOI: https://doi.org/10.1007/s12555-022-0590-x

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