Discussiones Mathematicae Differential Inclusions 19 (1999) 67-84

[BIBTex]

MATHEMATICAL MODEL AND OPTIMAL CONTROL OF FLOW INDUCED VIBRATION OF PIPELINES

N.U. Ahmed

School of Information Technology and Engineering
and Department of Mathematics, University of Ottawa
Ottawa, Canada

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.

Keywords: dynamic models, unitary group, semigroup, differential inclusions, vibration, optimal flow rate.

1991 Mathematics Subject Classification: 34K20, 35Q72, 93D05, 93D20.

References

[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] N.U. Ahmed and K.L. Teo, Optimal Control of Distributed Parameter Systems, Elsvier North Holland, New York, Oxford 1981.
[3] N.U. Ahmed, Optimal control of infinite dimensional systems governed by functional differential inclusions, Discuss. Math. Differential Inclusions 15 (1995), 75-94.
[4] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Vol 1: Theory, Kluwer Academic Publishers, Dordrecht, Boston, London 1997.
[5] M. Kisielewicz, Differential Inclusions and Optimal Control, PWN-Polish Scientific Publishers, Warsaw, Kluwer Academic Publishers, Dordrecht, Boston, London 1991.
[6] M. Roseau, Vibrations in Mechanical Systems, Springer-Verlag, Berlin Heidelberg, New York, London, Paris 1984.

Received 12 July 1999