Skip to main content
SpringerLink
Log in

Asymptotics of the optimal value of the performance functional for a rapidly stabilizing indirect control in the regular case

  • Ordinary Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

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

References

  1. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow, 1961.

  2. Krasovskii, N.N., Teoriya upravleniya dvizheniem (Theory of Motion Control), Moscow: Nauka, 1968.

    Google Scholar 

  3. Lie, E.B. and Markus, L., Foundations of Optimal Control Theory, New York: Wiley, 1967. Translated under the title Osnovy teorii optimal’nogo upravleniya, Moscow: Nauka, 1972.

    Google Scholar 

  4. Tikhonov, A.N., Mat. Sb., 1952, vol. 31(73), no. 3, pp. 575–586.

    Google Scholar 

  5. Kokotovic, P.V. and Jackel, R.A., IEEE Trans. Automat. Control, 1972, vol. 17, no. 1, pp. 29–37.

    Article  Google Scholar 

  6. Vasil’eva, A.B. and Dmitriev, M.G., Itogi Nauki Tekh. Ser. Mat. Analiz, 1982, vol. 20, pp. 3–77.

    MathSciNet  Google Scholar 

  7. Dontchev, A.L., Perturbations, Approximations and Sensitivity Analysis of Optimal Control Systems, Berlin: Springer, 1983. Translated under the title Sistemy optimal’nogo upravleniya: vozmushcheniya, priblizheniya i analiz chuvstvitel’nosti, Moscow: Mir, 1987.

    MATH  Google Scholar 

  8. Gabasov, R., Dmitruk, N.M., and Kirillova, F.M., Zh. Vychisl. Mat. Mat. Fiz., 2004, vol. 44, no. 3, pp. 444–466.

    MathSciNet  Google Scholar 

  9. Danilin, A.R. and Il’in, A.M., Izv. Akad. Nauk Tekhn. Kibern., 1994, no. 3, pp. 96–103.

  10. Danilin, A.R. and Il’in, A.M., Dokl. Akad. Nauk, 1996, vol. 350, no. 2, pp. 155–157.

    MathSciNet  Google Scholar 

  11. Kalinin, A.I. and Semenov, K.V., Zh. Vychisl. Mat. Mat. Fiz., 2004, vol. 44, no. 3, pp. 432–443.

    MathSciNet  Google Scholar 

  12. Dmitriev, M.G., Differ. Uravn., 1985, vol. 21, no. 10, pp. 1693–1698.

    MathSciNet  Google Scholar 

  13. Kalinin, A.I., Differ. Uravn., 1990, vol. 26, no. 4, pp. 585–594.

    MathSciNet  Google Scholar 

  14. Kiselev, Yu.N., Lineinaya teoriya bystrodeistviya s vozmushcheniyami (Linear Theory of Time Optimization with Perturbations), Moscow: Izdat. MGU, 1986.

    Google Scholar 

  15. Subbotin, A.I., Minimaksnye neravenstva i uravneniya Gamil’tona-Yakobi (Minimax Inequalities and Hamilton-Jacobi Equations), Moscow: Nauka, 1991.

    MATH  Google Scholar 

  16. Maslov, V.P. and Kolokol’tsev, V.N., Idempotentnyi analiz i ego primenenie v optimal’nom upravlenii (Idempotent Analysis and Its Applications to Optimal Control), Moscow: Nauka, 1994.

    Google Scholar 

  17. Subbotina, N.N., Prikl. Mat. Mekh., 1996, vol. 60, no. 6, pp. 901–908.

    MathSciNet  Google Scholar 

  18. Fan Ky, Proc. Nat. Acad. Sci. USA, 1953, vol. 39, pp. 42–47.

    Article  Google Scholar 

  19. Kurzhanskii, A.B., Upravlenie i nablyudenie v usloviyakh neopredelennosti (Control and Observation under Conditions of Indeterminacy), Moscow: Nauka, 1977.

    Google Scholar 

  20. Rockafellar, R., Convex Analysis, Princeton: Princeton University Press, 1970. Translated under the title Vypuklyi analiz, Moscow: Mir, 1973.

    MATH  Google Scholar 

  21. Ioffe, A.D. and Tikhomirov, V.M., Teoriya ekstremal’nykh zadach (Theory of Extremal Problems), Moscow: Nauka, 1974.

    Google Scholar 

  22. Danilin, A.R., Mat. Sb., 1998, vol. 189, no. 11, pp. 27–60.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

    A. R. Danilin

Authors
  1. A. R. Danilin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.R. Danilin, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 11, pp. 1473–1480.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Danilin, A.R. Asymptotics of the optimal value of the performance functional for a rapidly stabilizing indirect control in the regular case. Diff Equat 42, 1545–1552 (2006). https://doi.org/10.1134/S0012266106110048

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266106110048

Keywords

Search

Navigation