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Controllability and Reachability of Periodically Time-Variant Mixed-Valued Logical Control Networks

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Abstract

This paper investigates the controllability and reachability of periodically time-variant mixed-valued logical control networks (PTMLCNs). The PTMLCN considered in this paper consists of several mixed-valued logical control networks with periodically switching signals, which circulates among different mixed-valued logical control networks. First, a PTMLCN is transformed into a discrete dynamic system by the semi-tensor product. Based on this algebraic expression, the time-dependent input-state incident matrix and the time-dependent state transition matrix are defined and the relationship between these two matrices is given. Secondly, the controllability and reachability of PTMLCNs are defined. Subsequently, by virtue of the proposed matrices, a series of necessary and sufficient conditions are given for checking controllability and reachability, and the algorithm for finding the optimal control sequence to reach the target state in the shortest time is designed. Finally, the effectiveness of the proposed method is verified by an example.

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Data Availability Statement

The authors declare that the data supporting the findings of this study are available within the article.

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Authors and Affiliations

  1. The School of Mathematics, Shandong University, Jinan, 250100, People’s Republic of China

    Yakun Li, Jun-e Feng & Shuqian Zhu

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  1. Yakun Li
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  2. Jun-e Feng
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  3. Shuqian Zhu
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Correspondence to Jun-e Feng.

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This work was supported by the National Natural Science Foundation of China (61773371, 61877036, 61773238), and the Natural Science Foundation of Shandong Province (ZR2019MF002).

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Li, Y., Feng, Je. & Zhu, S. Controllability and Reachability of Periodically Time-Variant Mixed-Valued Logical Control Networks. Circuits Syst Signal Process 40, 3639–3654 (2021). https://doi.org/10.1007/s00034-021-01648-2

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  • DOI: https://doi.org/10.1007/s00034-021-01648-2

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