Skip to main content
Log in

On dual problems of optimal control

  • Determinate Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The common structure of duality of optimal control problems is suggested, which is based on the extension principle. The iterative computational algorithm is described, in which the primal and the dual problem are solved in parallel.

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. Pontryagin, L.S., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Nauka, 1976.

    Google Scholar 

  2. Krotov, V.F., Global Methods in Optimal Control Theory, New York: Marcel Dekker, 1996.

    MATH  Google Scholar 

  3. Gurman, V.I., Printsip rasshireniya v zadachakh upravleniya (The Extension Principle in Control Problems), Moscow: Nauka, 1997.

    MATH  Google Scholar 

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

    Google Scholar 

  5. Rockafellar, R.T., Convex Analysis, Princeton: Princeton Univ. Press, 1970. Translated under the title Vypuklyi analiz, Moscow: Mir, 1971.

    MATH  Google Scholar 

  6. Krotov, V.F., Methods of Solution of Variational Problems on the Basis of Sufficient Conditions of Absolute Minimum. I–III, Avtom. Telemekh., 1962, no. 12; 1963, no. 5; 1964, no. 7.

  7. Kolmogorov, A.N. and Fomin, S.V., Elementy teorii funktsii i funktsional’nogo analiza (Elements of the Theory of Functions and Functional Analysis), Moscow: Nauka, 1976.

    Google Scholar 

  8. Emel’yanov, S.V., Korovin, S.K., Bobylev, N.A., and Bulatov, A.V., Gomotopii ekstremal’nykh zadach (Homotopies of Extremal Problems), Moscow: Nauka, 2001.

    Google Scholar 

  9. Bobylev, N.A., Emel’yanov, S.V., and Korovin, S.K., Geometricheskie metody v variatsionnykh zadachakh (Geometric Methods in Variational Problems), Moscow: Magistr, 1998.

    Google Scholar 

  10. Vasil’ev, F.P., Chislennye metody resheniya ekstremal’nykh zadach (Numerical Methods of Solution of Extremal Problems), Moscow: Nauka, 1988.

    Google Scholar 

  11. Vasil’ev, F.P., Metody resheniya ekstremal’nykh zadach (Methods of Solution of Extremal Problems), Moscow: Nauka, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © A.V. Bulatov, V.F. Krotov, 2008, published in Avtomatika i Telemekhanika, 2008, No. 10, pp. 9–18.

This work was supported by the Russian Foundation for Basic Research, project no. 06-08-00586.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bulatov, A.V., Krotov, V.F. On dual problems of optimal control. Autom Remote Control 69, 1653–1662 (2008). https://doi.org/10.1134/S0005117908100020

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117908100020

PACS number

Navigation