Skip to main content
SpringerLink
Log in

Optimal control systems with state variable jump discontinuities

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

Abstract

Consideration is given to continuous-time, parameter-dependent optimal control problems with state-variable jump discontinuities atN variable interior times. A maximum principle involving known costate jump conditions is stated and is proved by transforming the problem into a standard Mayer control problem. An illustrative example for fisheries management is included.

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. Geering, H. P.,Continuous-Time Optimal Theory for Cost Functionals Including Discrete State Penalty Terms, IEEE Transactions on Automatic Control, Vol. AC-21, pp. 866–869, 1976.

    Google Scholar 

  2. Denbow, D. H.,A Generalized Form of the Problem of Bolza, University of Chicago, PhD Thesis, 1937.

  3. Bryson, A. E., andHo, Y. C.,Applied Optimal Control Theory, Ginn and Company, Waltham, Massachusetts, 1969.

    Google Scholar 

  4. Blaquière, A.,Differential Games with Piecewise Continuous Trajectories, Differential Games and Applications: Proceedings of a Workshop, Edited by P. Hagedorn, H. W. Knobloch, and G. J. Olsder, Springer-Verlag, Berlin, Germany, 1977.

    Google Scholar 

  5. Mason, J. D.,Transformations and Discontinuities for Optimal Space Trajectories, University of Arizona, PhD Thesis, 1968.

  6. Vincent, T. L., andMason, J. D.,Disconnected Optimal Trajectories, Journal of Optimization Theory and Applications, Vol. 3, pp. 263–281, 1969.

    Google Scholar 

  7. Hestenes, M. R.,Calculus of Variations and Optimal Control Theory, John Wiley and Sons, New York, New York, 1966.

    Google Scholar 

  8. Getz, W. M.,Optimal Harvesting of Structured Populations, National Research Institute for Mathematical Sciences, Pretoria, South Africa, Technical Report TWISK 23, 1978.

    Google Scholar 

  9. Jacobson, D. H., andMayne, D. Q.,Differential Dynamic Programming, American Elsevier Publishing Company, New York, New York, 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departments of Entomological Sciences and Plant Pathology, University of California, Berkeley, California

    W. M. Getz

  2. National Research Institute for Mathematical Sciences, CSIR, Pretoria, South Africa

    D. H. Martin (Director)

Authors
  1. W. M. Getz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. H. Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by G. Leitmann

This work was partially supported by a grant from Control Data. The authors are grateful to Professor T. L. Vincent for drawing their attention to Refs. 4–6 listed below.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Getz, W.M., Martin, D.H. Optimal control systems with state variable jump discontinuities. J Optim Theory Appl 31, 195–205 (1980). https://doi.org/10.1007/BF00934110

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00934110

Key Words

Search

Navigation