Abstract
We consider the inversion problem for linear systems, which involves estimation of the unknown input vector. The inversion problem is considered for a system with a vector output and a vector input assuming that the observed output is of higher dimension than the unknown input. The problem is solved by using a controlled model in which the control stabilizes the deviations of the model output from the system output. The stabilizing model control or its averaged form may be used as the estimate of the unknown system input.
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References
A. V. Il’in, S. K. Korovin, and V. V. Fomichev, “Inversion algorithms for linear dynamical system: controlled model method,” Different. Uravn., 33, 329–339 (1997).
A. V. Il’in, S. K. Korovin, and V. V. Fomichev, “Robust inversion of vector systems,” Different. Uravn., 34, No. 11, 1478–1486 (1998).
A. V. Il’in, S. K. Korovin, and V. V. Fomichev, “Controlled model method in dynamic system inversion,” Dokl. AN, Control Theory, 354, No. 2, 171–173 (1997).
H. H. Rosenbrock, “The zeros of a system,” Int. J. Contr., 18, No. 2, 297–299 (1973).
E. M. Smagina, Analysis of Linear Multidimensional Systems Using the Concept of the Zero of a System [in Russian], Izd. Tomsk Univ., Tomsk (1990).
Yu. N. Andreev, Control of Finite-Dimensional Linear Systems [in Russian], Nauka, Moscow (1976).
V. V. Fomichev, “Some inversion algorithms for linear dynamical systems,” in: Control and Identification Algorithms [in Russian], Dialog-MGU, Moscow (1997), pp. 156–167.
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Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 17–22, 2004.
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Il’in, A.V., Korovin, S.K. & Fomichev, V.V. Robust inversion algorithms for vector linear systems. Comput Math Model 19, 1–6 (2008). https://doi.org/10.1007/s10598-008-0001-z
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DOI: https://doi.org/10.1007/s10598-008-0001-z