Skip to main content
SpringerLink
Log in

Finite difference approximations to constrained optimal control problems

  • Part 2: Optimal Control
  • Conference paper
  • First Online:
Optimization and Optimal Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 30))

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bosarge W.E., Johnson O.G.: Error bounds of high order accuracy for the state regulator problem via piecewise polynomial approximation. SIAM J.Control, 9 /1971/, 15–28.

    Google Scholar 

  2. Budak, V.M. Vasil`ev F.P.: Some numerical aspects of optimal centrol problems. Izd. Moskovskogo Universiteta, Moscow 1975 / in Russian/

    Google Scholar 

  3. Cullum J. Finite-dimensional approximations of state-constrained continuous optimal control problems. SIAM J. Control, 10 /1972/, 649–670.

    Google Scholar 

  4. Ermol`ev Yu.M., Gulenko V.P. Tsarenko T.I.: Finite-difference method in optimal control problems. Naukova Dumka, Kiyev 1978 / in Russian/.

    Google Scholar 

  5. Gamkrelidze R.V.: On optimal sliding regimes.Dokl.AN SSSR, 143 /1962/, 1243–1246 /in Russian/.

    Google Scholar 

  6. Hager W.W.: Lipschitz continuity for constrained processes. SIAM J. Control and Optimization, 17 /1979/, 321–338.

    Google Scholar 

  7. Hager W.W.: Convex control and dual approximations.Pt I, II Control and Cybernetics, 8 /1979/, 6–22, 73–86.

    Google Scholar 

  8. Hager W.W., Ianculescu G.D.: Semi-dual approximations in optimal control / to appear/

    Google Scholar 

  9. Kurcyusz S.: On existence and nonexistence of Lagrange multipliers in Banach spaces. IOTA, 20 /1976/, 81–109.

    Google Scholar 

  10. Malanowski K.: On regularity of solutions to optimal control problems for systems with control appearing linearly. Arch. Aut. i Telemech., 23 /1978/, 227–242.

    Google Scholar 

  11. Malanowski K.: On normality of Lagrange multipliers for state and control constrained optimal control problems. Bull. Acad. Pol. Ser. Tech., 26 /1978/, 529–535.

    Google Scholar 

  12. Malanowski K.: On convergence of finite difference approximations to optimal control problems for systems with control appearing linearly. Arch. Aut. i Telemech., 24 /1979/, 155–171.

    Google Scholar 

  13. Malanowski K.: On convergence of finite difference approximations to control and state constrained convex optimal control problems. Arch. Aut. i Telemech. 24 /1979/, 319–337.

    Google Scholar 

  14. Mathis F.H., Reddien G.W.: Ritz-Trefftz approximations in optimal control. SIAM J. Control and Optimization, 17 /1979/, 307–310.

    Google Scholar 

  15. Mordukhovich B.Sh.: On finite difference approximations of optimal control systems. Prikl. Mat. i Mekh., 42 /1978/ 431–440 /in Russian/

    Google Scholar 

  16. Warga J.: Optimal control of differential and functional equations. Academic Press, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Systems Research Institute Polish Academy of Sciences, ul. Newelska 6, 01-447, Warszawa

    Kazimierz Malanowski

Authors
  1. Kazimierz Malanowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alfred Auslender Werner Oettli Josef Stoer

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Malanowski, K. (1981). Finite difference approximations to constrained optimal control problems. In: Auslender, A., Oettli, W., Stoer, J. (eds) Optimization and Optimal Control. Lecture Notes in Control and Information Sciences, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004519

Download citation

  • DOI: https://doi.org/10.1007/BFb0004519

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10627-2

  • Online ISBN: 978-3-540-38591-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation