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Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

ISSN 印刷: 1064-2315
ISSN オンライン: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v50.i11.10
pages 1-18

Guaranteed Estimation of Nonstationary Parameters of Difference Equations under Uncertainty

Alexander G. Nakonechnyi
Kiev National Taras Shevchenko University, Kiev
Petr N. Zinko
Kiev National Taras Shevchenko University, Kiev
Yulia M. Shevchuk
Kiev National Taras Shevchenko University, Kiev

要約

The algorithms of building optimal and guaranteed estimations of nonstationary parameters of difference nonlinear equations with additive noise are given. The approaches to construct optimal estimations based on Bellman functions and Kalman–Bussi filter are presented. The results of numerical experiments for the problem of building guaranteed and optimal estimates for mathematical model of spreading one type of information are considered. The offered approach except theoretical interest has an important practical meaning.

参考

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  2. Gubarev V.F., Shevchenko V.N., Gummel А.V., State estimation for systems subjected to bounded uncertainty using moving horizon approach, Prep. Of the 15-lh IFAC Symposium on system identification, July 6-8, 2009, Saint-Malo, France, 2009, 910–915.

  3. Bakan G.M., Ellipsoidal algorithms of guaranteed estimation and the recurrent least squares method in problems for filtering states of dynamical systems, “Problemy upravleniya i informatiki”, 2000, No. 3, 34–48.

  4. Kuntsevich V.M., Control under the conditions of uncertainty: guaranteed results in control and identification problems, Kiev, Naukova dumka, 2006.

  5. Nakonechny A.G., Parameter estimation under conditions of uncertainty, Nauchnyye zapiski Kiyevskogo natsionalnogo universiteta im. Tarasa Shevchenko, 2004, 7, 102–111.

  6. Nakonechny A.G., Tasks of guaranteed estimation of parameters in dynamics, Tezisy XVII Mezhdunarodnoy konferentsii “Problems of decision making under uncertainties”, May 23–27, 2011, Skhodnitsa, Ukraine, 2011, 141.

  7. Nakonechny A.G., Zinko P.M., Shevchuk Yu.M., Forecast estimates in mathematical models of dissemination of information under uncertainty, Sistemnyye issledovaniya i informatsionnyye tekhnologii, 2017, No. 4, 54–65, DOI: 10.20535/SRIT.2308-8893.2017.4.0.

  8. Nakonechny A.G., Zinko P.M., Shevchuk Yu.M., Analysis of nonstationary mathematical models of information dissemination under uncertainty, Tezisy mezhdunarodnoy konferentsii “Sovremennyye problemy matematicheskogo modelirovaniya, vychislitelnykh metodov i informatsionnykh tekhnologiy”.

  9. Nakonechny O.G., Zinko P.M., Shevchuk Yu.M., Estimate of parameters of difference equations under uncertainty, Proceedings of “Ukrainian conference on applied mathematics”, September, 28–30, 2017, Lviv, Ukraine, 2017, 182–184.

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