Skip to main content
SpringerLink
Log in

Attainability problems under stochastic perturbations

  • 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. Varaiya, P. and Kurzhanskii, A.B., Dokl. RAN, 2000, vol. 372, no. 4, pp. 446–450.

    Google Scholar 

  2. Kurzhanski, A.B. and Varaiya, P., SIAM J. on Contr. & Optim., 2002, vol. 41, no. 1, pp. 181–216.

    Google Scholar 

  3. Lygeros, J., Tomlin, C., and Sastry, S., Automat., 1999, vol. 535, no. 3, pp. 349–370.

    Google Scholar 

  4. Lygeros, J. and Watkins, O., Proc. 42nd IEEE Conf. on Decision and Control. Maui, Hawaii, USA, December 2003, pp. 5314–5319.

  5. Åström, K.J., Introduction to Stochastic Control Theory, New York: Academic, 1970. Translated under the title Vvedenie v stokhasticheskuyu teoriyu upravleniya, Moscow, 1973.

    Google Scholar 

  6. Fleming, W.H. and Rishel, R.W., Deterministic and Stochastic Optimal Control, Berlin: Springer, 1975. Translated under the title Optimal’noe upravlenie determinirovannymi i stokhasticheskimi sistemami, Moscow: Mir, 1978.

    Google Scholar 

  7. Fleming, W.H. and Soner, H.M., Controlled Markov Processes and Viscosity Solutions, New York, 1993.

  8. Liptser, R. Sh. and Shiryaev, A.N., Statistika sluchainykh protsessov (Statistics of Random Processes), Moscow: Nauka, 1974.

    Google Scholar 

  9. Kurzhanskii, A.B., Differents. Uravn., 1965, vol. 1, no. 2, pp. 204–213.

    Google Scholar 

  10. Levy, P., Processus stochastiques et mouvement brownien, Paris: Gauthier-Villars, 1965. Translated under the title Stokhasticheskie protsessy i brounovskoe dvizhenie, Moscow: Nauka, 1972.

    Google Scholar 

  11. Bertsekas, D.P., Dynamic Programming, Athena Scientific, Belmont, Mass., 1995, vol. 1–2.

    Google Scholar 

  12. Krasovskii, N.N., Prikl. Mat. Mekh., 1960, vol. 24, no. 1, pp. 64–79.

    Google Scholar 

  13. Krasovskii, N.N., Sib. Mat. Zh., 1963, vol. 4, no. 3, pp. 622–631.

    Google Scholar 

  14. Kats, I. Ya. and Kurzhanskii, A.B., Avtomat. Telemekh., 1970, no. 12, pp. 15–25.

    Google Scholar 

  15. Kurzhanski, A.B. and Váalyi, I., Ellipsoidal Calculus for Estimation and Control, Boston, 1997.

  16. Aubin, J.-P. and Da Prato, G., Stoch. Anal. & App., 1998, no. 16, pp. 1–15.

    Google Scholar 

  17. Bensoussan, A., Da Prato, G., Delfour, M.C., and Mitter, S.K., Representation and Control of Infinite Dimensional Systems, Boston, 1992, vol. 1; 1993, vol. 2.

  18. Dar’in, A.N. and Kurzhanskii, A.B., Differents. Uravn., 2001, vol. 37, no. 11, pp. 1477–1484.

    Google Scholar 

  19. Kurzhanski, A.B. and Varaiya, P., Optimiz. Meth. & Software, 2002, vol. 17, pp. 177–237.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    I. A. Digailova & A. B. Kurzhanskii

Authors
  1. I. A. Digailova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. B. Kurzhanskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Differentsial’nye Uravneniya, Vol. 40, No. 11, 2004, pp. 1494–1499.

Original Russian Text Copyright ©2004 by Digailova, Kurzhanskii.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Digailova, I.A., Kurzhanskii, A.B. Attainability problems under stochastic perturbations. Diff Equat 40, 1573–1578 (2004). https://doi.org/10.1007/s10625-005-0069-6

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10625-005-0069-6

Keywords

Search

Navigation