Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T01:56:45.845Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Optimal Control of a Class of Time-DelaySystem

Published online by Cambridge University Press:  26 August 2010

A. Taik ,
L. Boudjenah  and
M.F. Khelfi
Get access

Abstract

In this work we study the optimal control problem for a class of nonlinear time-delaysystems via paratingent equation with delayed argument. We use an equivalence theorembetween solutions of differential inclusions with time-delay and solutions of paratingentequations with delayed argument. We study the problem of optimal control which minimizes acertain cost function. To show the existence of optimal control, we use the maintopological properties of the set solutions of paratingent equation with delayedargument

Keywords

differential inclusionminimizationoptimal controlparatingenttime-delay
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 7: JANO9 – The 9thInternational Conference on Numerical Analysis and Optimization , 2010 , pp. 151 - 155
Copyright
© EDP Sciences, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

J. P.Aubin, A. Cellina. Differential inclusions, Springer-Verlag, 1984.
Boudjenah, L.. Existence of the solutions of the paratingent equation with delayed argument . Electron. J. Diff. Eqns., 2005 (2005), No. 14, 1–8.Google Scholar
Dadebo, S., Luus, R.. Optimal control of time-delay systems by dynamic programming . Optim Control Appl. Methods, 13 (1992), No. 1, 29–41.CrossRefGoogle Scholar
M.Kisielewicz. Differential inclusions and optimal control. Kluwer, Dordrecht, The Netherlands, (1991).
Y. Kuang. Delay differential equations with applications in population dynamics. Academic Press, Boston, (1993).
ygmunt, W... On some properties of a certain family of solutions of the paratingent equation . Ann. Univ. Marie Curie-Sklodowska, Lublin. Polonia. Sect. A, 28 (1976), 136–141.Google Scholar