In this paper, a minimum time problem for n×n co-operative hyperbolic systems involving Laplace operator and with time-delay is considered. First, the existence of a unique solution of such hyperbolic system with time-delay is proved. Then necessary conditions of a minimum time control are derived in the form of maximum principle. Finally the bang-bang principle and the approximate controllability conditions are investigated.
| Published in | Mathematics Letters (Volume 3, Issue 1) |
| DOI | 10.11648/j.ml.20170301.11 |
| Page(s) | 1-11 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2017. Published by Science Publishing Group |
Time-Optimal Control Problem, Co-operative Systems, Hyperbolic Systems with Time Delay, Approximate Controllability, Bang-Bang Principle
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APA Style
Hussein El-Saify, Mohammed Shehata. (2017). Minimum Time Problem for n×n Co-operative Hyperbolic Lag Systems. Mathematics Letters, 3(1), 1-11. https://doi.org/10.11648/j.ml.20170301.11
ACS Style
Hussein El-Saify; Mohammed Shehata. Minimum Time Problem for n×n Co-operative Hyperbolic Lag Systems. Math. Lett. 2017, 3(1), 1-11. doi: 10.11648/j.ml.20170301.11
AMA Style
Hussein El-Saify, Mohammed Shehata. Minimum Time Problem for n×n Co-operative Hyperbolic Lag Systems. Math Lett. 2017;3(1):1-11. doi: 10.11648/j.ml.20170301.11
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Download@article{10.11648/j.ml.20170301.11,
author = {Hussein El-Saify and Mohammed Shehata},
title = {Minimum Time Problem for n×n Co-operative Hyperbolic Lag Systems},
journal = {Mathematics Letters},
volume = {3},
number = {1},
pages = {1-11},
doi = {10.11648/j.ml.20170301.11},
url = {https://doi.org/10.11648/j.ml.20170301.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20170301.11},
abstract = {In this paper, a minimum time problem for n×n co-operative hyperbolic systems involving Laplace operator and with time-delay is considered. First, the existence of a unique solution of such hyperbolic system with time-delay is proved. Then necessary conditions of a minimum time control are derived in the form of maximum principle. Finally the bang-bang principle and the approximate controllability conditions are investigated.},
year = {2017}
}
TY - JOUR T1 - Minimum Time Problem for n×n Co-operative Hyperbolic Lag Systems AU - Hussein El-Saify AU - Mohammed Shehata Y1 - 2017/03/30 PY - 2017 N1 - https://doi.org/10.11648/j.ml.20170301.11 DO - 10.11648/j.ml.20170301.11 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 1 EP - 11 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20170301.11 AB - In this paper, a minimum time problem for n×n co-operative hyperbolic systems involving Laplace operator and with time-delay is considered. First, the existence of a unique solution of such hyperbolic system with time-delay is proved. Then necessary conditions of a minimum time control are derived in the form of maximum principle. Finally the bang-bang principle and the approximate controllability conditions are investigated. VL - 3 IS - 1 ER -
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