Robust filtering for joint state-parameter estimation in distributed mechanical systems

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January & February 2009, 23(1&2): 65-84. doi: 10.3934/dcds.2009.23.65

Robust filtering for joint state-parameter estimation in distributed mechanical systems

Dominique Chapelle ^1, , Philippe Moireau ^1, and Patrick Le Tallec ^2,

1.	INRIA, B.P. 105, 78153 Le Chesnay cedex, France, France
2.	Ecole Polytechnique, 91128 Palaiseau cedex, France

Received December 2007 Revised April 2008 Published September 2008

Abstract
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We present an effective filtering procedure for jointly estimating state variables and parameters in a distributed mechanical system. This method is based on a robust, low-cost filter related to collocated feedback and used to estimate state variables, and an H ^∞ setting is then employed to formulate a joint state-parameter estimation filter. In addition to providing a tractable filtering approach for an infinite-dimensional mechanical system, the H ^∞ setting allows to consider measurement errors that cannot be handled by Kalman type filters, e.g. for measurements only available on the boundary. For this estimation strategy a complete error analysis is given, and a detailed numerical assessment -- using a test problem inspired from cardiac biomechanics -- demonstrates the effectiveness of our approach.

Keywords: estimation; robust filtering; solid continuum mechanics; numerical analysis.

Mathematics Subject Classification: 35R30, 93B36, 74H15.

Citation: Dominique Chapelle, Philippe Moireau, Patrick Le Tallec. Robust filtering for joint state-parameter estimation in distributed mechanical systems. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 65-84. doi: 10.3934/dcds.2009.23.65

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