Skip to main content
SpringerLink
Log in
Book cover

Trends in Mathematical Optimization pp 43–54Cite as

Equivalent Perturbations and Approximations in Optimal Control

  • Chapter

  • 516 Accesses

Abstract

We present a characterization of the continuity of the optimal value (marginal function) of optimal control problems to differential inclusions with respect to the data. Extending our method we study the convergence of finite difference approximations and of the penalty function method for reduction of the state constraints.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berge C., Espaces topologiques. Functions multivoques. Dunod, Paris 1966.

    Google Scholar 

  2. Budak B. M., Vasil’ev F.P., Some computational aspects of optimal control problems. Moscow Univ. Press, Moscow 1975.

    Google Scholar 

  3. Cullum J., Perturbations of optimal control problems. SIAM J. Control 4 (1966), 473–487.

    Article  Google Scholar 

  4. Giôev T., Well-posedness of optimal control problems with integral convex performance index. Serdica 2 (1976), 334–342.

    Google Scholar 

  5. Dontchev A. L., MordukhoviC B. S., Relaxation and well-posedness of nonlinear optimal processes. Systems and Contr. Letters 3 (1983), 177–179.

    Article  Google Scholar 

  6. Dontchev A. L., Perturbations, approximations and sensitivity analysis of optimal control systems. Springer 1983.

    Google Scholar 

  7. Kirillova F. M., On the continuous dependence of the solutions of an optimal control problem with respect to the initial data and parameters. Uspekhi Math. Nauk 17 (1962) 4(106).

    Google Scholar 

  8. Kokotovic P., Applications of singular perturbation techniques to control problems. SIAM Review 26 (1984), 501–549.

    Article  Google Scholar 

  9. Tadumadze T. A., Some topics of qualitative theory of optimal control. Tbilissi Univ. Press, Tbilissi 1983.

    Google Scholar 

  10. Taubert K., Converging multistep methods for initial value problems involving multivalued maps. Computing 27 (1981), 123–136.

    Article  Google Scholar 

  11. Warga J., Relaxed variational problems. J. Math. Anal. Appl. 4 (1962), 111–128.

    Article  Google Scholar 

  12. Zolezzi T., Well-posedness and stability analysis in optimization. Proc. Journées Fermât, Toulouse 1985 (to appear).

    Google Scholar 

  13. Mordukhovii B. S., On the finite-dimensional approximations to optimal control systems. Prikl. Math. Mech. 42 (1978), 431–440.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Bulgarian Acad. of Sciences, 1113, Sofia, Acad. G. Bonchev 8, Bulgaria, UK

    A. L. Dontchev

Authors
  1. A. L. Dontchev
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, Memminger Straße 6, D-8900, Augsburg, Germany

    Karl-Heinz Hoffmann

  2. Mathematisches Institut, Universität Bayreuth, Universitätsstrasse 30, D-8580, Bayreuth, Germany

    Jochem Zowe

  3. U.F.R. Mathématiques, Informatique, Université Paul Sabatier, 118, Route de Narbonne, F-31062, Toulouse Cédex, France

    Jean-Baptiste Hiriart-Urruty

  4. INRIA, Rocquencourt, F-78153, Le Chesnay, France

    Claude Lemarechal

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Birkhäuser Verlag Basel

About this chapter

Cite this chapter

Dontchev, A.L. (1988). Equivalent Perturbations and Approximations in Optimal Control. In: Hoffmann, KH., Zowe, J., Hiriart-Urruty, JB., Lemarechal, C. (eds) Trends in Mathematical Optimization. International Series of Numerical Mathematics/Internationale Schriftenreihe zur Numerischen Mathematik/Série internationale d’Analyse numérique, vol 84. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9297-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-9297-1_3

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9984-0

  • Online ISBN: 978-3-0348-9297-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation