Skip to main content
SpringerLink
Log in

Infinite-horizon stable control of a parabolic equation

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

The control of a parabolic equation is considered. The solution of this equation is assumed to be measured inaccurately. An algorithm is described for finding a feedback control function such that the solution of this equation tracks the solution of another equation generated by an unknown right-hand side.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. Gajewski, K. Gröger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen (Akademie, Berlin, 1974; Mir, Moscow, 1978).

    MATH  Google Scholar 

  2. J.-L. Lions, Quelques méthodes de résolution des problémes aux limites non linéires (Dunod, Paris, 1969; Mir, Moscow, 1972).

    Google Scholar 

  3. A. Bensoussan, G. Da Prato, M. Delfour, and S. Mitter, Representation and Control of Infinite Dimensional Systems (Birkhäuser, Boston, 1992).

    MATH  Google Scholar 

  4. V. Barbu, Optimal Control of Variational Inequalities (Pitman, London, 1984).

    MATH  Google Scholar 

  5. N. N. Krasovskii and A. I. Subbotin, Game-Theoretical Control Problems (Nauka, Moscow, 1974; Springer-Verlag, New York, 1988).

    Google Scholar 

  6. Yu. S. Osipov, “Feedback control in parabolic systems,” Prikl. Mat. Mekh. 41 (2), 195–201 (1977).

    Google Scholar 

  7. Yu. S. Osipov, Selected Works (Mosk. Gos. Univ., Moscow, 2009) [in Russian].

    Google Scholar 

  8. V. I. Maksimov, “On tracking solutions of parabolic equations,” Russ. Math. 56 (1), 35–42 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  9. V. I. Maksimov, “Regularized extremal shift in problems of stable control,” System Modeling and Optimization: 25th IFIP TC 7 Conference, CSMO 2011, Berlin, Germany, September 12–16, 2011, Ed. by D. Hömberg and F. Tröltzsch (Springer, Berlin, 2013), pp. 112–121.

    Chapter  Google Scholar 

  10. Yu. S. Osipov and A. V. Kryazhimskii, Inverse Problems for Ordinary Differential Equations: Dynamical Solutions (Gordon and Breach, London, 1995).

    MATH  Google Scholar 

  11. Yu. S. Osipov, F. P. Vasil’ev, and M. M. Potapov, Basics of the Dynamic Regularization Method (Mosk. Gos. Univ., Moscow, 1999) [in Russian].

    Google Scholar 

  12. A. V. Kryazhimskii and V. I. Maksimov, “Resource-saving infinite-horizon tracing under uncertain input,” Appl. Math. Comput. 217, 1135–1140 (2010).

    Article  MathSciNet  Google Scholar 

  13. A. V. Kryazhimskiy and V. I. Maksimov, “Resource-saving tracking problem with infinite time horizon,” Differ. Equations 47 (7), 1004–1013 (2011).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    M. S. Blizorukova

  2. Ural Federal University, ul. Mira 19, Yekaterinburg, 620002, Russia

    M. S. Blizorukova

Authors
  1. M. S. Blizorukova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. S. Blizorukova.

Additional information

Original Russian Text © M.S. Blizorukova, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 9, pp. 1503–1510.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Blizorukova, M.S. Infinite-horizon stable control of a parabolic equation. Comput. Math. and Math. Phys. 55, 1461–1467 (2015). https://doi.org/10.1134/S0965542515090067

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542515090067

Keywords

Search

Navigation