American Institute of Mathematical Sciences

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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

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