Skip to main content
Log in

Problem of tracking in linear systems with parametric uncertainties under unstable zero dynamics

  • Robust and Adaptive Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Proposed was a solution to the problem of tracking in linear SISO systems with unstable zero dynamics in the conditions of parametric uncertainty of the models of plant and reference generator under incomplete information about the state vectors. The approach developed employs the methods of the sliding mode theory in the problems of real-time feedback design, observation, and parameter identification.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Wonham, W.M., Linear Multivariable Control: A Geometric Approach, New York: Springer, 1979. Translated under the title Linei’nye mnogomernye sistemy upravleniya: Geometricheskii podkhod, Moscow: Nauka, 1980.

    MATH  Google Scholar 

  2. Marino, R. and Santosuosso, G.L., Regulation of Linear Systems with Unknown Exosystems of Uncertain Order, IEEE Trans. Automat. Control, 2007, vol. 52, no. 2, pp. 352–359.

    Article  MathSciNet  Google Scholar 

  3. Utkin, V.A., Invariance and Independence in Systems with Separable Motion, Autom. Remote Control, 2001, vol. 62, no. 11, pp. 1825–1843.

    Article  MathSciNet  MATH  Google Scholar 

  4. Utkin, A.V., Method of State Expansion in the Design of Autonomous Control, Autom. Remote Control, 2007, vol. 68, no. 6, pp. 1006–1022.

    Article  MathSciNet  MATH  Google Scholar 

  5. Utkin, V.I., Skol’zyashchie rezhimy v zadachakh optimizatsii i upravleniya, Moscow: Nauka, 1981. Translated into English under the title Sliding Modes in Control Optimization, Heidelberg: Springer, 1992.

    Google Scholar 

  6. Utkin, V.A., Method of Separation of Motions in Observation Problems, Autom. Remote Control, 1990, vol. 51, no. 3, part 1, pp. 300–309.

    MathSciNet  MATH  Google Scholar 

  7. Krasnova, S.A., Utkin, V.A., and Mikheev, Y.V., Cascade Design of State Observers, Autom. Remote Control, 2001, vol. 62, no. 2, pp. 207–225.

    Article  MathSciNet  MATH  Google Scholar 

  8. Akhobadze, A.G. and Krasnova, S.A., Tracking in Linear MIMO Systems under External Perturbations, Autom. Remote Control, 2009, vol. 70, no. 6, pp. 933–957.

    Article  MathSciNet  MATH  Google Scholar 

  9. Utkin, V.I., Principle of Identification on Sliding Modes, Dokl. Akad. Nauk SSSR, 1981, vol. 257, no. 3, pp. 558–561.

    MathSciNet  Google Scholar 

  10. Drakunov, S.V., Izosimov, D.B., Luk’yanov, A.G., Utkin, V.A., and Utkin, V.I., The Block Control Principle. I, Autom. Remote Control, 1990, vol. 51, no. 5, part 1, pp. 601–609.

    MathSciNet  MATH  Google Scholar 

  11. Krasnova, S.A., Sirotina, T.G., and Utkin, V.A., A Structural Approach to Robust Control, Autom. Remote Control, 2011, vol. 72, no. 8, pp. 1639–1666.

    Article  MathSciNet  MATH  Google Scholar 

  12. Andreev, Yu.N., Upravlenie konechnomernymi lineinymi ob”ektami (Control of Finite-dimensional Linear Plants), Moscow: Nauka, 1976.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. A. Utkin.

Additional information

Original Russian Text © V.A. Utkin, A.V. Utkin, 2014, published in Avtomatika i Telemekhanika, 2014, No. 9, pp. 45–64.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Utkin, V.A., Utkin, A.V. Problem of tracking in linear systems with parametric uncertainties under unstable zero dynamics. Autom Remote Control 75, 1577–1592 (2014). https://doi.org/10.1134/S0005117914090045

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117914090045

Keywords

Navigation