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Distributed Delays in State and Control and Linear Delay Systems: Ideal Control
Subject area: Science,Engineering and Technology · Area of research: Applied Mathematics
Abstract
In order to prove the existence and uniqueness of optimum control for linear delay systems with distributed delays in state and control, the paper builds on the work of [6]. It is demonstrated that the optimal control is distinct and, assuming the system is reasonably controllable, takes the following form:
Keywords
Optimal Control, Linear Delays, Distributed Delays, Null Controllability.
References
[1] N. Eke and C. A. Nse: Optimal Control of Neutral Systems with a Non – linear Base, the maximum principle perspective; Journal of the Nigerian Association of Mathematical Physics, Vol. 11, 2007.
[2] A. Nse: Stability of Discrete Control Systems, Journal of the Nigerian Association of Mathematical Physics, Vol. 10, 2006.
[3] E. N. Chukwu: The Time Optimal Control Theory of Linear Differential Equations of Neutral Type. Journal of Computational Mathematics and Applications Vol. 16 No. 10/11 Great Britain 1988.
[4] H. Hermes and J. P Lasalle: Functional Analysis and Time Optimal Control. Academic press, New York 1969.
[5] J. Klamka: Relative Controllability and Minimum Energy Control of Linear Systems with Distributed Delays in Control, IEEE Trans Automatic Control, Ac – 21, 1976, pp. 594 – 595.S
[6] J. U. Onwuatu: Optimal Control of Discrete Delay Systems. Journal of the Nigerian Mathematical Society, Vol. 19, 2000.
[7] M. Robinson: Stability Theory for Systems of Inequalities Differential Non – linear systems – SIAM Journal of Numerical Analysis 13 (4), 1976.
[8] V. A. Iheagwam and J. U. Onwuatu: Relative Controllability and Null Controllability of Linear Delay System with Distributed Delays in the State and Control. Journal of the Nigerian Association of Mathematical Physics, Vol 9, 2008.
[9] V. A. Iheagwam: The Minimum Control Energy Problem for Differential Systems with Distributed Delays in Control, Journal of the Nigerian Mathematical Society Vol. 21, 2002.
[10] W.E. Brunday: On the asymptotic behavior of solutions of differential difference equations of neutral type, Journal of Differential equations, 258 – 274, 1977.
How to cite this paper
@article{1710036,
author = {Faket K. Namah, Charles O. Aminobiren},
title = {Distributed Delays in State and Control and Linear Delay Systems: Ideal Control},
journal = {Iconic Research And Engineering Journals},
year = {2025},
volume = {9},
number = {2},
pages = {515-521},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1710036.pdf},
abstract = {In order to prove the existence and uniqueness of optimum control for linear delay systems with distributed delays in state and control, the paper builds on the work of [6]. It is demonstrated that the optimal control is distinct and, assuming the system is reasonably controllable, takes the following form:},
keywords = {Optimal Control, Linear Delays, Distributed Delays, Null Controllability.},
month = {August},
}