Symmetry-based observers for some water-tank problems

Abstract : In this paper we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surfac e height is measured. The fluid motion is described by shallow water equations in two horizontal dimensions. We build a simple non-linear observer which takes advantage of the symmetries of fluid dynamics laws. As a result its structure is based on convolutions with smooth isotropic kernels, and the observer is remarkably robust to noise. We prove the convergence of the observer around a steady-state. In numerical applications local exponential convergence is expected. The observer is also applied to the problem of predicting the ocean circulation. Realistic simulations illustrate the relevance of the approach compared with some standard oceanography techniques.
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Contributor : Didier Auroux <>
Submitted on : Friday, November 15, 2013 - 4:44:44 PM
Last modification on : Monday, November 12, 2018 - 10:56:16 AM

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  • HAL Id : hal-00905013, version 1

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Didier Auroux, Silvère Bonnabel. Symmetry-based observers for some water-tank problems. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2011, 56 (5), pp.1046-1058. 〈hal-00905013〉

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