Minimum Time Problem for n×n Co-operative Hyperbolic Lag Systems
Mathematics Letters
Volume 3, Issue 1, February 2017, Pages: 1-11
Received: Dec. 17, 2016; Accepted: Dec. 30, 2016; Published: Mar. 30, 2017
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Authors
Hussein El-Saify, Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
Mohammed Shehata, Department of Mathematics, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia
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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.
Keywords
Time-Optimal Control Problem, Co-operative Systems, Hyperbolic Systems with Time Delay, Approximate Controllability, Bang-Bang Principle
To cite this article
Hussein El-Saify, Mohammed Shehata, Minimum Time Problem for n×n Co-operative Hyperbolic Lag Systems, Mathematics Letters. Vol. 3, No. 1, 2017, pp. 1-11. doi: 10.11648/j.ml.20170301.11
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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