Abstract
We consider the problem of inversion of a dynamical system, that is, the problem of reconstructing the unknown input of a system on the basis of the measured output. To form a continuous estimate of the unknown input, we suggest to use a controlled model of the system in which the control is constructed with the use of higher-order sliding modes.
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Il’in, A.V., Korovin, S.K., and Fomichev, V.V., Algorithms for the Inversion of Linear Scalar Dynamical Systems: the Controlled Model Method, Differ. Uravn., 1997, vol. 33, no. 3, pp. 329–339.
Korovin, S.K., Il’in, A.V., and Fomichev, V.V., The Controllable Model Method in Problems of the Inversion of Dynamical Systems, Dokl. Akad. Nauk Teor. Upravl., 1997, vol. 354, no. 2, pp. 171–173.
Il’in, A.V., Korovin, S.K., and Fomichev, V.V., Inversion Algorithms for Linear Control Systems, Differ. Uravn., 1997, vol. 33, no. 6, pp. 744–750.
Il’in, A.V., Korovin, S.K., and Fomichev, V.V., Robust Inversion of Vector Linear Systems, Differ. Uravn., 1998, vol. 34, no. 11, pp. 1478–1486.
Il’in, A.V., Emel’yanov, S.V., and Fomichev, V.V., Synthesis of Robust Inverters of Minimum Order, Differ. Uravn., 2009, vol. 45, no. 4, pp. 575–585.
Il’in, A.V., Korovin, S.K., and Fomichev, V.V., Metody robastnogo obrashcheniya dinamicheskikh sistem (Methods of Robust Inversion of Dynamical Systems), Moscow, 2009.
Il’in, A.V., Korovin, S.K., and Fomichev, V.V., Inversion of Linear Dynamical Systems with Delay, Differ. Uravn., 2012, vol. 48, no. 3, pp. 405–413.
Osipov, Yu.S. and Kryazhimskii, A.V., Modeling of a Control in a Dynamical System, Izv. Akad. Nauk SSSR Tekhn. Kibern., 1983, vol. 269, no. 2, pp. 51–60.
Osipov, Yu.S. and Kryazhimskii, A.V., Dynamic Solution of Operator Equations, Izv. Akad. Nauk SSSR Tekhn. Kibern., 1983, vol. 269, no. 3, pp. 552–556.
Emel’yanov, S.V. and Korovin, S.K., Novye tipy obratnoi svyazi (New Types of Feedback), Moscow: Nauka, 1997.
Utkin, V.I., Skol’zyashchie rezhimy i ikh primeneniya v sistemakh s peremennoi strukturoi (Sliding Modes and Their Applications in Variable Structure Systems), Moscow: Nauka, 1974.
Emel’yanov, S.V., Korovin, S.K., and Levantovskii, L.V., Higher-Order Sliding Modes in Control Systems, in Nelineinye dinamicheskie sistemy: kachestvennyi analiz i upravlenie: Sb. trudov (Nonlinear Dynamical Systems: Qualitative Analysis and Control: Collection of Papers), 1993, no. 2, pp. 39–70.
Emel’yanov, S.V., Korovin, S.K., and Levantovskii, L.V., A New Class of Second-Order Sliding Algorithms, Mat. Model., 1990, vol. 2, no. 3, pp. 89–100.
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Original Russian Text © D.A. Vasin, A.V. Il’in, V.V. Fomichev, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 11, pp. 1471–1476.
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Vasin, D.A., Il’in, A.V. & Fomichev, V.V. Inversion of dynamical systems with the use of higher-order sliding modes. Diff Equat 50, 1466–1471 (2014). https://doi.org/10.1134/S0012266114110056
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DOI: https://doi.org/10.1134/S0012266114110056