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		Jinde CHANG.[en_title][J].Control Theory and Technology,2008,6(2):127~132.[Copy]

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JindeCHANG
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Received:December 20, 2006Revised:April 23, 2007

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Identification of variable coefficients for vibrating systems by boundary control and observation

Jinde CHANG

(Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100080, China; Graduate University of Chinese Academy of Sciences, Beijing 100049, China)

Abstract:

We consider the identification problem of coefficients for vibrating systems described by a Euler-Bernoulli beam equation or a string equation, with one end clamped and with an input exerted on the other end. For the beam equation, the observations are the velocity and the angle velocity at the free end, while for the string equation, the observation is the velocity at the free end. In the framework of well-posed linear system theory, we show that both the density and the flexural rigidity of the beam, and the tension of the string, can be uniquely determined by the observations for all positive times. Moreover, a general constructive method is developed to show that the mass density and the elastic modulus of the string are not determined by the observation.

Key words: Beam equation Identifiability Well-posedness Variable coefficients Inverse problem