Abstract
Parametric estimation under uncertainty of the plant model description was considered within the framework of the ellipsoidal approach to the problems of guaranteed estimation. The unknown multidimensional plant whose parameter vector should be estimated was assumed to be linear and static, and uncertainty of its “input-output” model, to have both additive and multiplicative components. The external ellipsoidal approximations of the nonconvex information sets guaranteeing that the vector of possible plant parameters is contained in them were constructed from the results of observations. The method of their construction comes to semidefinite programming, that is, to minimization of the linear function constrained by the linear matrix inequalities which are readily realized by the numerical methods.
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Original Russian Text © S.A. Nazin, B.T. Polyak, 2007, published in Avtomatika i Telemekhanika, 2007, No. 6, pp. 67–80.
This work was supported in part by the grant MK-1294.2005.8 of the President of the Russian Federation, Russian Foundation for Basic Research, project no. 05-01-00114, and the Complex Program no. 22 for Basic Research of the Presidium of the Russian Academy of Sciences.
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Nazin, S.A., Polyak, B.T. Ellipsoid-based parametric estimation in the linear multidimensional systems with uncertain model description. Autom Remote Control 68, 993–1005 (2007). https://doi.org/10.1134/S0005117907060070
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DOI: https://doi.org/10.1134/S0005117907060070