Skip to main content
Log in

Dual variational principles with deviating argument and discontinuous extremals

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

Abstract

We study dual or complementary variational principles for functionals with deviating argument and discontinuous extremals. Local conditions for the existence of a pair of dual extremum principles are given. Results are then applied to the control problem involving linear neutral differential-difference equations.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. El'sgol'c, L. E.,Qualitative Methods of Mathematical Analysis, Translations of Mathematical Monographs, Vol. 12, American Mathematical Society, Providence, Rhode Island, 1964.

    Google Scholar 

  2. Hughes, D. K.,Variational and Optimal Control Problems with Delayed Argument, Journal of Optimization Theory and Applications, Vol. 2, pp. 1–14, 1968.

    Google Scholar 

  3. Sabbagh, L. D.,Variational Problems with Lags, Journal of Optimization Theory and Applications, Vol. 3, pp. 34–51, 1969.

    Google Scholar 

  4. Halanay, A.,Variational Problems with Delayed Argument, Delay and Functional Differential Equations, Theory and Applications, Edited by K. Schmitt, Academic Press, New York, New York, 1973.

    Google Scholar 

  5. Kamenskii, G. A.,Variational and Boundary-Value Problems with Deviating Argument, Differential Equations, Vol. 6, pp. 1026–1032, 1970.

    Google Scholar 

  6. Kamenskii, G. A.,On Extrema of Functionals with Deviating Arguments, Soviet Mathematics, Vol. 16, pp. 1380–1383, 1975.

    Google Scholar 

  7. Noble, B.,Complementary Variational Principles for Boundary Value Problems, I: Basic Principles with an Application to Ordinary Differential Equations, University of Wisconsin, Mathematics Research Center, Report No. 473, 1964.

  8. Arthurs, A. M.,Complementary Variational Principles, Clarendon Press, Oxford, England, 1970.

    Google Scholar 

  9. Chan, W. L.,Dual Variational Principles with Delayed Argument, International Journal of Control, Vol. 20, pp. 1015–1019, 1974.

    Google Scholar 

  10. Chan, W. L.,Variational Dualities in the Linear Regulator and Estimation Problems with and without Time Delay, Journal of the Institute of Mathematics and Its Applications, Vol. 18, pp. 237–247, 1976.

    Google Scholar 

  11. Aggarwal, J. K., andEller, D. H.,Optimal Control of Neutral Systems, International Journal of Control, Vol. 14, pp. 309–319, 1971.

    Google Scholar 

  12. Conner, M. A.,A Gradient Method for Neutral Systems, Automatica, Vol. 9, pp. 639–641, 1973.

    Google Scholar 

  13. Datko, R.,Neutral Autonomous Functional Equations with Quadratic Cost, SIAM Journal on Control, Vol. 12, pp. 70–82, 1974.

    Google Scholar 

  14. Palm, W. J., andSchmitendorf, W. E.,Conjugate Points Conditions for Variational Problems with Delayed Argument, Journal of Optimization Theory and Applications, Vol. 14, pp. 599–612, 1974.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by D. F. Lawden

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chan, W.L., Tai, C.H. Dual variational principles with deviating argument and discontinuous extremals. J Optim Theory Appl 23, 593–605 (1977). https://doi.org/10.1007/BF00933299

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00933299

Key Words

Navigation