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Limit set problem of multi-agent systems with finite states: An eigenvalue-based approach

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Abstract

This paper studies the limit set of multi-agent system with finite states, in which the system is converted into a linear system through an expansion of space. Then, the structure properties of the system matrix are investigated, and the relationships between the eigenvalues and the limit set are developed. As an application, the nilpotent problem of elementary cellular automata (ECA) known as algorithmically undecidable is considered, and all the nilpotent ECA are found out which consists of rules 0, 8, 64, 239, 253, 255.

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Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China

    Lin Wang & Xiaofan Wang

  2. Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai, 200240, China

    Lin Wang & Xiaofan Wang

  3. School of Sciences, Hebei University of Technology, Tianjin, 300000, China

    Jinhuan Wang

Authors
  1. Lin Wang
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  2. Xiaofan Wang
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  3. Jinhuan Wang
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Corresponding author

Correspondence to Lin Wang.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 61473189, 61374176, 61203142 and 61203073, a Doctoral Program of High Education of China under Grant No. 20110073120027, and partly by the Excellent Young Technology Innovation Foundation of Hebei University of Technology under Grant No. 2012005.

This paper was recommended for publication by Editor HAN Jing.

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Wang, L., Wang, X. & Wang, J. Limit set problem of multi-agent systems with finite states: An eigenvalue-based approach. J Syst Sci Complex 28, 570–579 (2015). https://doi.org/10.1007/s11424-015-3061-0

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  • DOI: https://doi.org/10.1007/s11424-015-3061-0

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