Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-04T08:03:46.769Z Has data issue: false hasContentIssue false
  • English
  • Français

On the existence of piecewise continuous optimal controls

Published online by Cambridge University Press:  17 February 2009

E. S. Noussair
E. S. Noussair
Affiliation:
School of Mathematics, University of New South Wales, Sydney, N.S.W., 2033, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Existence of piecewise optimal control is proved when the cost function includes one or both of (a) a cost of sudden switching (discontinuity) of control variables, and (b) a cost associated with the maximum rate of variation of the control over segments of the path for which the control is continuous.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 1 , June 1977 , pp. 31 - 37
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Hermes, H. and Salle, J. P. La, Functional Analysis and Time Optimal Control, Mathematics in Science and Engineering, Vol. 56, Academic Press, New York and London (1969).CrossRefGoogle Scholar
[2]Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V. and Mishchenko, E. F., The Mathematical Theory of Optimal Processes, Gosudarst, Miscow, 1961; English transl. Interscience, New York (1962), Pergamon Press, New York (1964).Google Scholar
[3]Cesari, L., “An existence theorem in problems of optimal control”, J. SIAM Control, Ser. A, Vol. 3, No. 1 (1965).Google Scholar
[4]Noussair, E. S. and Blatt, J. M., “Optimal control with costs of rapid variation of control” (submitted).Google Scholar
[5]Lee, E. B. and Markus, L., Foundations of Optimal Control Theory, The SIAM Series in Applied Mathematics, John Wiley and Sons, New York, London and Sydney (1967).Google Scholar