Skip to main content
Log in

On optimal control problem for moving sources for a parabolic equation

  • Systems Theory and General Control Theory
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

A variational method for solving an optimal control problem for moving sources for systems, their states described by a parabolic-type equation, is considered. The necessary optimality conditions are found in the form of pointwise and integral maximum principles. The theoretical conclusions are illustrated by a numerical example.

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. A. G. Butkovskii, Control Methods for Systems with Distributed Parameters (Nauka, Moscow, 1975) [in Russian].

    Google Scholar 

  2. A. G. Butkovskii and L. M. Pustyl’nikov, Theory of Moving Control of Systems with Distributed Parameters (Nauka, Moscow, 1980) [in Russian].

    Google Scholar 

  3. J. L. Lions, Controle optimal de systemes gouvernes par des equations aux derivees partielles (Gauther-Villars, Paris, 1968) [in French].

    MATH  Google Scholar 

  4. R. A. Teymurov, “On existence and uniqueness of solution of moving sources optimal control problem,” Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerbaijan 31 (39), 219–224 (2009).

    MathSciNet  MATH  Google Scholar 

  5. B. T. Bilalov and R. A. Teymurov, “Necessary conditions of optimality in a distributed parameters system,” Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerbaijan 32 (40), 91–100 (2010).

    MathSciNet  MATH  Google Scholar 

  6. R. A. Teymurov, “Study of one class problems of optimal control by moving sources in systems with the distributed parameters,” Trans. Natl. Acad. Sci. Azerbaijan, Ser. Phys.-Tech. Math. Sci. 32 (4), 117–126 (2012).

    MathSciNet  MATH  Google Scholar 

  7. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic (Nauka, Moscow, 1976) [in Russian].

    MATH  Google Scholar 

  8. O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics, Appl. Math. Sci., Vol. 49 (Nauka, Moscow, 1973; Springer, New York, 1985).

  9. A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems (Nauka, Moscow, 1974; Halsted, New York, 1977).

    MATH  Google Scholar 

  10. F. P. Vasil’ev, Methods of Extreme Problems Solution (Nauka, Moscow, 1981).

    Google Scholar 

  11. A. A. Samarskii, The Theory of Differential Schemes (Nauka, Moscow, 1989; Marcel Dekker, New York, 2001).

    Book  MATH  Google Scholar 

  12. V. P. Mikhailov, Partial Differential Equations (Nauka, Moscow, 1983).[in Russian].

    Google Scholar 

  13. K. Yoshida, Functional Analysis, Springer Classics in Mathematics, 6th ed. (Springer, Berlin, Heidelberg, 1996).

    Google Scholar 

  14. M. Goebel, “On existence of optimal control,” Math. Nachr. 93, 67–73 (1979).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. A. Teymurov.

Additional information

Original Russian Text © R.A. Teymurov, 2016, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2016, No. 2, pp. 19–28.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Teymurov, R.A. On optimal control problem for moving sources for a parabolic equation. J. Comput. Syst. Sci. Int. 55, 179–188 (2016). https://doi.org/10.1134/S1064230716020064

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064230716020064

Keywords

Navigation