Skip to main content
SpringerLink
Log in

New Existence Result for Autonomous One-Dimensional Optimal Control Problems

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

The approach to optimal control problems based on a purely variational reformulation may lead to new existence results by using fine, general existence theorems for variational problems without convexity assumptions. We illustrate this perspective here for autonomous one-dimensional problems and defer the study of more complex situations to later work.

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

Similar content being viewed by others

References

  1. Buttazzo, G., Giaquinta, M., Hildebrandt, S.: One-Dimensional Variational Problems. Oxford University Press, Oxford (1998)

    MATH  Google Scholar 

  2. Cesari, L.: Optimization Theory and Applications. Springer, Berlin (1983)

    MATH  Google Scholar 

  3. Ornelas, A.: Existence of scalar minimizers for autonomous simple integrals nonconvex except at zero. Nonlinear Anal. (2007, in press)

  4. Ornelas, A.: Existence and regularity for scalar minimizers of affine nonconvex simple integrals. Nonlinear Anal. 53, 441–451 (2003)

    Article  MATH  Google Scholar 

  5. Ekeland, I., Temam, R.: Analyse convèxe et problems variationnels. Dunod, Gauthier-Villars, Paris (1974)

    Google Scholar 

  6. Pedregal, P.: On the generality of variational principles. Milan J. Math. 71, 19–356 (2003)

    Article  Google Scholar 

  7. Bellido, J., Pedregal, P.: Optimal design via variational principles: the one-dimensional case. J. Math. Pure Appl. 80, 245–261 (2001)

    Article  MATH  Google Scholar 

  8. Aubin, J.: Set-Valued Analysis. Birkhäuser, Boston (1990)

    MATH  Google Scholar 

  9. Fusco, N., Marcellini, P., Ornelas, A.: Existence of minimizers for some nonconvex one-dimensional integrals. Portugal. Math. 55, 167–184 (1998)

    MATH  Google Scholar 

  10. Rudin, W.: Real and Complex Analysis. McGraw-Hill, New York (1987)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, ETSI Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain

    P. Pedregal

  2. EST Barreiro, Instituto Politécnico de Setúbal, Barreiro, Portugal

    J. Tiago

Authors
  1. P. Pedregal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Tiago
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Tiago.

Additional information

Communicated by N.G. Medhin.

This research was supported by Project MTM2004-07114 from Ministerio de Educación y Ciencia (Spain) and by Grant PAI05-029 from JCCM (Castilla-La Mancha).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pedregal, P., Tiago, J. New Existence Result for Autonomous One-Dimensional Optimal Control Problems. J Optim Theory Appl 134, 241–255 (2007). https://doi.org/10.1007/s10957-007-9227-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-007-9227-8

Keywords

Search

Navigation