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System identification under saturated precise or set-valued measurements

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Abstract

This paper considers the system identification problem based on saturated precise or set-valued measurements, which is widely used in various fields and has essential difficulties. Since existing methodologies cannot make full use of the mixed data, this paper is aiming to fill the gap and build a unified framework in dealing with such problems rigorously and comprehensively. New algorithms are introduced and their properties are established. Most significantly, the Cramér-Rao (CR) lower bound based on the measurements is established, which consists of two parts with respect to the precise data and set-valued data, respectively. This prompts the idea of designing an estimation algorithm by grouping and combining the estimations under two classifications of data. As a result, a CR lower bound-based algorithm (CRBA) is constructed. The convergence properties are theoretically analyzed in terms of consistency and asymptotic efficiency under periodic inputs. For general inputs, an algorithm based on the CRBA that combines the expectation maximization (EM) algorithm for set-valued subsystems and the gradient descent algorithm for precise subsystems is proposed. Numerical simulations validate the superiority of the proposed algorithms.

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Acknowledgements

This work was supported by National Key R&D Program of China (Grant No. 2018YFA0703800), National Natural Science Foundation of China (Grant No. 62025306), and CAS Project for Young Scientists in Basic Research (Grant No. YSBR-008).

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Authors and Affiliations

  1. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yanlong Zhao & Hang Zhang

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yanlong Zhao & Hang Zhang

  3. Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing, 100083, China

    Ting Wang

  4. Department of Biostatistics, St. Jude Children’s Research Hospital, Memphis, TN, 38105, USA

    Guolian Kang

Authors
  1. Yanlong Zhao
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  2. Hang Zhang
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  3. Ting Wang
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  4. Guolian Kang
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Correspondence to Yanlong Zhao.

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Zhao, Y., Zhang, H., Wang, T. et al. System identification under saturated precise or set-valued measurements. Sci. China Inf. Sci. 66, 112204 (2023). https://doi.org/10.1007/s11432-021-3505-5

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  • DOI: https://doi.org/10.1007/s11432-021-3505-5

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