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Inversion of dynamical systems with the use of higher-order sliding modes

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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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References

  1. 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.

    MathSciNet  Google Scholar 

  2. 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.

    MathSciNet  Google Scholar 

  3. 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.

    Google Scholar 

  4. 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.

    MathSciNet  MATH  Google Scholar 

  5. 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.

    MathSciNet  Google Scholar 

  6. 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.

    MATH  Google Scholar 

  7. 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.

    MathSciNet  Google Scholar 

  8. 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.

    MathSciNet  Google Scholar 

  9. 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.

    MathSciNet  Google Scholar 

  10. Emel’yanov, S.V. and Korovin, S.K., Novye tipy obratnoi svyazi (New Types of Feedback), Moscow: Nauka, 1997.

    Google Scholar 

  11. 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.

    Google Scholar 

  12. 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.

    Google Scholar 

  13. 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.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Control Problems, Russian Academy of Sciences, Moscow, Russia

    D. A. Vasin, A. V. Il’in & V. V. Fomichev

  2. Institute of Systems Analysis, Russian Academy of Sciences, Moscow, Russia

    D. A. Vasin, A. V. Il’in & V. V. Fomichev

  3. Moscow State University, Moscow, Russia

    D. A. Vasin, A. V. Il’in & V. V. Fomichev

Authors
  1. D. A. Vasin
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  2. A. V. Il’in
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  3. V. V. Fomichev
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Correspondence to D. A. Vasin.

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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

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