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Comparative Analysis of Optimal Filters of the Second and Third Order for Continuous-Time Systems

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Abstract

We consider the problem of constructing functional filters (optimal functional observers, i.e., observers for linear functionals of the state vector) for linear time-invariant control systems in which the inhomogeneity contains additive white noise as a term in addition to control. The output of the system is linear in the state vector and also contains additive white noise as a term. With the help of canonical representations, a comparative analysis of the second- and third-order filters by the mean square observation error in the steady state is carried out. An example of a fourth-order system is given, showing that with an increase in the dynamic order of the filter, the optimality by a quadratic criterion increases.

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Funding

The article was published with the financial support of the Ministry of Education and Science of the Russian Federation within the framework of the program of the Mathematical Center for Fundamental and Applied Mathematics under agreement no. 075-15-2019-1621 and with the financial support of the Russian Foundation for Basic Research, projects nos. 20-37-90065-Aspiranty and 20-08-00073-A.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, China

    V. V. Fomichev

  2. Lomonosov Moscow State University, Moscow, 119991, Russia

    V. V. Fomichev & M. A. Kamenshchikov

  3. Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

    V. V. Fomichev

  4. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    M. A. Kamenshchikov

  5. National University of Science and Technology “MISiS”, Moscow, 119049, Russia

    M. A. Kamenshchikov

Authors
  1. V. V. Fomichev
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  2. M. A. Kamenshchikov
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Corresponding authors

Correspondence to V. V. Fomichev or M. A. Kamenshchikov.

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Translated by V. Potapchouck

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Fomichev, V.V., Kamenshchikov, M.A. Comparative Analysis of Optimal Filters of the Second and Third Order for Continuous-Time Systems. Diff Equat 57, 1527–1535 (2021). https://doi.org/10.1134/S0012266121110112

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  • DOI: https://doi.org/10.1134/S0012266121110112

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