# American Institute of Mathematical Sciences

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

 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.
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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