Mathematical model and optimal control of flow induced vibration of pipelines

N.U. Ahmed

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1999)

  • Volume: 19, Issue: 1-2, page 67-84
  • ISSN: 1509-9407

Abstract

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In this paper we consider a dynamic model for flow induced vibration of pipelines. We study the questions of existence and uniqueness of solutions of the system. Considering the flow rate as the control variable, we present three different necessary conditions of optimality. The last one with state constraint involves Differential Inclusions. The paper is concluded with an algorithm for computing the optimal controls.

How to cite

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N.U. Ahmed. "Mathematical model and optimal control of flow induced vibration of pipelines." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 19.1-2 (1999): 67-84. <http://eudml.org/doc/276010>.

@article{N1999,
abstract = {In this paper we consider a dynamic model for flow induced vibration of pipelines. We study the questions of existence and uniqueness of solutions of the system. Considering the flow rate as the control variable, we present three different necessary conditions of optimality. The last one with state constraint involves Differential Inclusions. The paper is concluded with an algorithm for computing the optimal controls.},
author = {N.U. Ahmed},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {dynamic models; unitary group; semigroup; differential inclusions; vibration; optimal flow rate; existence; dynamic model; flow induced vibration of pipelines; uniqueness; conditions of optimality},
language = {eng},
number = {1-2},
pages = {67-84},
title = {Mathematical model and optimal control of flow induced vibration of pipelines},
url = {http://eudml.org/doc/276010},
volume = {19},
year = {1999},
}

TY - JOUR
AU - N.U. Ahmed
TI - Mathematical model and optimal control of flow induced vibration of pipelines
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1999
VL - 19
IS - 1-2
SP - 67
EP - 84
AB - In this paper we consider a dynamic model for flow induced vibration of pipelines. We study the questions of existence and uniqueness of solutions of the system. Considering the flow rate as the control variable, we present three different necessary conditions of optimality. The last one with state constraint involves Differential Inclusions. The paper is concluded with an algorithm for computing the optimal controls.
LA - eng
KW - dynamic models; unitary group; semigroup; differential inclusions; vibration; optimal flow rate; existence; dynamic model; flow induced vibration of pipelines; uniqueness; conditions of optimality
UR - http://eudml.org/doc/276010
ER -

References

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  1. [1] N.U. Ahmed, Semigroup Theory with Applications to Systems and Control, Pitman Research Notes in Mathematics Series, vol. 246, Longman Scientific and Technical, U.K, Co-published with John Wiley, New York, USA 1991. 
  2. [2] N.U. Ahmed and K.L. Teo, Optimal Control of Distributed Parameter Systems, Elsvier North Holland, New York, Oxford 1981. 
  3. [3] N.U. Ahmed, Optimal control of infinite dimensional systems governed by functional differential inclusions, Discuss. Math. Differential Inclusions 15 (1995), 75-94. Zbl0824.49007
  4. [4] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Vol 1: Theory, Kluwer Academic Publishers, Dordrecht, Boston, London 1997. Zbl0887.47001
  5. [5] M. Kisielewicz, Differential Inclusions and Optimal Control, PWN-Polish Scientific Publishers, Warsaw, Kluwer Academic Publishers, Dordrecht, Boston, London 1991. Zbl0731.49001
  6. [6] M. Roseau, Vibrations in Mechanical Systems, Springer-Verlag, Berlin Heidelberg, New York, London, Paris 1984. 

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