Skip to main content
Log in

R.V. Gamkrelidze’s maximum principle for optimal control problems with bounded phase coordinates and its relation to other optimality conditions

  • Control Theory
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

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.

References

  1. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1983; Gordon and Breach, New York, 1986).

    MATH  Google Scholar 

  2. R. V. Gamkrelidze, Dokl. Akad. Nauk SSSR 125, 475–478 (1959).

    MathSciNet  MATH  Google Scholar 

  3. R. V. Gamkrelidze, Izv. Akad. Nauk SSSR 24, 315–356 (1960).

    MathSciNet  MATH  Google Scholar 

  4. A. Ya. Dubovitskii and A. A. Milyutin, Dokl. Akad. Nauk SSSR 149, 759–762 (1963).

    Google Scholar 

  5. A. V. Arutyunov and N. T. Tynyanskii, Izv. Akad. Nauk SSSR, Ser. Tekh. Kibern., No. 4, 60–68 (1984).

  6. A. V. Arutyunov, Extremum Conditions: Abnormal and Degenerate Problems (Faktorial, Moscow, 1997) [in Russian].

    MATH  Google Scholar 

  7. A. V. Arutyunov, Dokl. Akad. Nauk SSSR 280, 1033–1037 (1985).

    MathSciNet  Google Scholar 

  8. A. Ya. Dubovitskii and V. A. Dubovitskii, Usp. Mat. Nauk 40(2), 175–176 (1985).

    MathSciNet  Google Scholar 

  9. A. V. Arutyunov, Dokl. Akad. Nauk SSSR 304, 11–14 (1989).

    MathSciNet  Google Scholar 

  10. R. Vinter, Optimal Control (Birkhäuser, Boston, 2000).

    MATH  Google Scholar 

  11. A. V. Arutyunov and N. Yu. Chernikova, “On the Controllability of Trajectories in Optimal Control Problems with State Constraints,” in Advances in Science and Technology: Modern Mathematics and Applications (VINITI, Moscow, 1999), Vol. 64, pp. 49–56 [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Arutyunov.

Additional information

Original Russian Text © A.V. Arutyunov, D.Yu. Karamzin, F. Pereira, 2011, published in Doklady Akademii Nauk, 2011, Vol. 436, No. 6, pp. 738–742.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arutyunov, A.V., Karamzin, D.Y. & Pereira, F. R.V. Gamkrelidze’s maximum principle for optimal control problems with bounded phase coordinates and its relation to other optimality conditions. Dokl. Math. 83, 131–135 (2011). https://doi.org/10.1134/S1064562411010285

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562411010285

Keywords

Navigation