On the Optimal Control of a Class of Time-Delay System

L. Boudjenah; M.F. Khelfi

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 151-155
  • ISSN: 0973-5348

Abstract

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In this work we study the optimal control problem for a class of nonlinear time-delay systems via paratingent equation with delayed argument. We use an equivalence theorem between solutions of differential inclusions with time-delay and solutions of paratingent equations with delayed argument. We study the problem of optimal control which minimizes a certain cost function. To show the existence of optimal control, we use the main topological properties of the set solutions of paratingent equation with delayed argument

How to cite

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Boudjenah, L., and Khelfi, M.F.. Taik, A., ed. "On the Optimal Control of a Class of Time-Delay System." Mathematical Modelling of Natural Phenomena 5.7 (2010): 151-155. <http://eudml.org/doc/197658>.

@article{Boudjenah2010,
abstract = {In this work we study the optimal control problem for a class of nonlinear time-delay systems via paratingent equation with delayed argument. We use an equivalence theorem between solutions of differential inclusions with time-delay and solutions of paratingent equations with delayed argument. We study the problem of optimal control which minimizes a certain cost function. To show the existence of optimal control, we use the main topological properties of the set solutions of paratingent equation with delayed argument},
author = {Boudjenah, L., Khelfi, M.F.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {differential inclusion; minimization; optimal control; paratingent; time-delay},
language = {eng},
month = {8},
number = {7},
pages = {151-155},
publisher = {EDP Sciences},
title = {On the Optimal Control of a Class of Time-Delay System},
url = {http://eudml.org/doc/197658},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Boudjenah, L.
AU - Khelfi, M.F.
AU - Taik, A.
TI - On the Optimal Control of a Class of Time-Delay System
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 151
EP - 155
AB - In this work we study the optimal control problem for a class of nonlinear time-delay systems via paratingent equation with delayed argument. We use an equivalence theorem between solutions of differential inclusions with time-delay and solutions of paratingent equations with delayed argument. We study the problem of optimal control which minimizes a certain cost function. To show the existence of optimal control, we use the main topological properties of the set solutions of paratingent equation with delayed argument
LA - eng
KW - differential inclusion; minimization; optimal control; paratingent; time-delay
UR - http://eudml.org/doc/197658
ER -

References

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  1. J. P.Aubin, A. Cellina. Differential inclusions, Springer-Verlag, 1984.  Zbl0538.34007
  2. L. Boudjenah. Existence of the solutions of the paratingent equation with delayed argument. Electron. J. Diff. Eqns., 2005 (2005), No. 14, 1–8. Zbl1075.34054
  3. S. Dadebo, R. Luus. Optimal control of time-delay systems by dynamic programming. Optim Control Appl. Methods, 13 (1992), No. 1, 29–41. Zbl0776.49021
  4. M.Kisielewicz. Differential inclusions and optimal control. Kluwer, Dordrecht, The Netherlands, (1991).  Zbl0731.49001
  5. Y. Kuang. Delay differential equations with applications in population dynamics. Academic Press, Boston, (1993).  Zbl0777.34002
  6. W.. ygmunt. 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. 

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