Skip to main content
Log in

Optimality conditions in a step control problem

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

Abstract

First-and second-order necessary optimality conditions are obtained for the control of step systems.

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

Access this article

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Similar content being viewed by others

References

  1. L. T. Ashchepkov, Optimal Control of Discontinuous Systems (Nauka, Novosibirsk, 1987) [in Russian].

    MATH  Google Scholar 

  2. V. A. Baturin, V. A. Dykhta, et al., Solution Methods for Control Theory Problems Based on the Expansion Principle (Nauka, Novosibirsk, 1990) [in Russian].

    Google Scholar 

  3. I. A. Agofonova, L. L. Gulin, and I. V. Rasina, Mathematical Modeling and Optimization of the Methylation of Sulfaminoantipyrine Disodium Salt, Available from VINITI, No. 3457 (Irkutsk, 1978).

  4. V. V. Velichenko, “Optimal Control of Composite Systems,” Dokl. Akad. Nauk SSSR 176, 754–765 (1967).

    MATH  MathSciNet  Google Scholar 

  5. S. B. Kirichenko, “Optimal Control of Systems with Intermediate Phase Constraints,” Kibern. Sist. Anal., No. 4, 104–111 (1994).

  6. K. B. Mansimov and Sh. F. Magerramov, “Second-Order Necessary Conditions for Optimality in a Discrete System with Variable Structure,” Zh. Bil’gi, Ser. Fiz. Mat., No. 1, 61–64 (2001).

  7. K. B. Mansimov and Sh. F. Magerramov, Preprint IK NAN Az. (Natl. Acad. Sci. of Azerbaijan, Baku, 2001).

    Google Scholar 

  8. Sh. F. Magerramov, “Krotov-Type Sufficient Optimality Condition for a Class of Discrete Systems with Variable Structure,” Zh. Bil’gi, Ser. Fiz., Mat., No. 2, 36–41 (2000).

  9. G. K. Zakharov, “Optimization of Step Control Systems,” Avtom. Telemekh., No. 8, 5–9 (1981).

  10. Sh. Sh. Yusubov, Preprint No. 20, BGU (Baku State Univ., Baku, 2000).

  11. G. K. Zakharov, “Optimization of Step Systems with Controllable Transition Conditions,” Avtom. Telemekh., No. 6, 32–36 (1993).

  12. K. B. Mansimov, “On Optimality of Singular (in Classical Sense) Controls in Systems with Delay,” Differ. Uravn., No. 3, 527–530 (1985).

  13. K. B. Mansimov, “Multipoint Necessary Optimality Conditions for Quasi-Singular Controls,” Avtom. Telemekh., No. 10, 53–58 (1982).

  14. K. B. Mansimov, Singular Controls in Systems with Delay (ELM, Baku, 1999) [in Russian].

    Google Scholar 

  15. R. Gabasov and F. M. Kirillova, Singular Optimal Controls (Nauka, Moscow, 1973) [in Russian].

    Google Scholar 

  16. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1969; Gordon & Breach, New York, 1986).

    Google Scholar 

  17. R. Gabasov and F. M. Kirillova, Optimization of Linear Systems (Belarus. Gos. Univ., Minsk, 1973) [in Russian].

    Google Scholar 

  18. V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control (Nauka, Moscow, 1979) [in Russian].

    MATH  Google Scholar 

  19. R. Gabasov and F. M. Kirillova, “On the Theory of Necessary Optimality Conditions of High Order,” Differ. Uravn., No. 4, 646–651 (1970).

  20. R. Gabasov and F. M. Kirillova, “On the Theory of Necessary Optimality Conditions of Singular Controls,” Dokl. Akad. Nauk SSSR 183, 300–302 (1968).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © R.R. Ismailov, K.B. Mansimov, 2006, published in Zhumal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 10, pp. 1758–1770.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ismailov, R.R., Mansimov, K.B. Optimality conditions in a step control problem. Comput. Math. and Math. Phys. 46, 1674–1686 (2006). https://doi.org/10.1134/S0965542506100058

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542506100058

Keywords

Navigation