Skip to main content
SpringerLink
Log in

An Euler–Lagrange Inclusion for Optimal Control Problems with State Constraints

  • Published:
Journal of Dynamical and Control Systems Aims and scope Submit manuscript

Abstract

New first-order necessary conditions for optimality for control problems with pathwise state constraints are given. These conditions are a variant of a nonsmooth maximum principle which includes a joint subdifferential of the Hamiltonian – a condition called Euler–Lagrange inclusion (ELI). The main novelty of the result provided here is the ability to address state constraints while using an ELI.

The ELI conditions have a number of desirable properties. Namely, they are, in some cases, able to convey more information about minimizers, and for the normal convex problems they are sufficient conditions of optimality. It is shown that these strengths are retained in the presence of state constraints.

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. M. d. R. de Pinho and R.B. Vinter, An Euler–Lagrange inclusion for optimal control problems. IEEE Trans. Automat. Control 40 (1995), 1191–1198.

    Google Scholar 

  2. R. B. Vinter, Optimal control. Birkhäuser, 2000.

  3. R.B. Vinter and G. Pappas, A maximum principle for nonsmooth optimal-control problems with state constraints. J. Math. Anal. Appl. 89 (1982), 212–232.

    Google Scholar 

  4. F. H. Clarke, Optimization and nonsmooth analysis. Wiley, New York, 1983. Republished: Classics in Applied Mathematics. SIAM, vol. 5, 1990.

  5. B. S. Mordukhovich, Approximation methods in problems of optimization and control. (Russian) Nauka, Moscow (to appear in Wiley– Interscience, the 2nd edition), 1988.

  6. R.T. Rockafellar and B. Wets, Variational analysis. Springer, Berlin, 1998.

    Google Scholar 

  7. R. F. Hartl, S.P. Sethi, and R.G. Vickson, A survey of the maximum principles for optimal control problems with state constraints. SIAM Rev. 37 (1995), No. 2, 181–218.

    Google Scholar 

  8. L. W. Neustadt, Optimization, a theory of necessary conditions. Princeton Univ. Press, 1976.

  9. F. H. Clarke, The maximum principle under minimal hypotheses. SIAM J. Control Optim. 14 (1976), No. 6, 1078–1091.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ISR and DEEC, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    M.D.R. De Pinho & M.M.A. Ferreira

  2. Departamento de Matemática, CMAT, Universidade do Minho, 4800-058, Guimarães, Portugal

    F.A.C.C. Fontes

Authors
  1. M.D.R. De Pinho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M.M.A. Ferreira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F.A.C.C. Fontes
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

De Pinho, M., Ferreira, M. & Fontes, F. An Euler–Lagrange Inclusion for Optimal Control Problems with State Constraints. Journal of Dynamical and Control Systems 8, 23–45 (2002). https://doi.org/10.1023/A:1013948616436

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013948616436

Keywords

Search

Navigation