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

Mathematical Modelling of Natural Phenomena (2010)

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

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topBoudjenah, 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

top- J. P.Aubin, A. Cellina. Differential inclusions, Springer-Verlag, 1984. Zbl0538.34007
- 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
- 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
- M.Kisielewicz. Differential inclusions and optimal control. Kluwer, Dordrecht, The Netherlands, (1991). Zbl0731.49001
- Y. Kuang. Delay differential equations with applications in population dynamics. Academic Press, Boston, (1993). Zbl0777.34002
- 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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