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Finite-Time Observability of Probabilistic Logical Control Systems

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Abstract

This study investigates finite-time observability of probabilistic logical control systems (PLCSs) under three definitions (i.e., finite-time observability with probability one, finite-time single-input sequence observability with probability one, and finite-time arbitrary-input observability with probability one). The authors adopt a parallel extension technique to recast the finite-time observability problem of a PLCS as a finite-time set reachability problem. Then, the finite-time set reachability problem can be transferred to stabilization problem of a logic dynamical system by using the state transfer graph reconstruction method. Necessary and sufficient conditions for finite-time observability under the three definitions are derived respectively. Finally, the proposed methods are illustrated by numerical examples.

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Authors and Affiliations

  1. School of Information Engineering, Nanchang University, Nanchang, 330031, China

    Rongpei Zhou

  2. School of Automation, Central South University, Changsha, 410083, China

    Yuqian Guo & Weihua Gui

  3. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G 1, Canada

    Xinzhi Liu

Authors
  1. Rongpei Zhou
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  2. Yuqian Guo
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  3. Xinzhi Liu
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  4. Weihua Gui
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Corresponding author

Correspondence to Rongpei Zhou.

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The authors declare no conflict of interest.

Additional information

This work was jointly supported by the National Natural Science Foundation of China under Grant Nos. 62103178, 61873284 and 61321003, and NSERC Canada.

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Cite this article

Zhou, R., Guo, Y., Liu, X. et al. Finite-Time Observability of Probabilistic Logical Control Systems. J Syst Sci Complex 36, 1905–1926 (2023). https://doi.org/10.1007/s11424-023-2013-3

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  • DOI: https://doi.org/10.1007/s11424-023-2013-3

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