Symmetry-Based Observers for Some Water-Tank Problems
In this paper, we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surface height is measured. The fluid motion is described by shallow water equations in two horizontal dimensions. We build a simple nonlinear observer which takes advantage of the symme...
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| Veröffentlicht in: | IEEE transactions on automatic control 2011-05, Vol.56 (5), p.1046-1058 |
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| creator | Auroux, D Bonnabel, S |
| description | In this paper, we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surface height is measured. The fluid motion is described by shallow water equations in two horizontal dimensions. We build a simple nonlinear 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. |
| doi_str_mv | 10.1109/TAC.2010.2067291 |
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The fluid motion is described by shallow water equations in two horizontal dimensions. We build a simple nonlinear 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. 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The fluid motion is described by shallow water equations in two horizontal dimensions. We build a simple nonlinear 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. 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Character string processing</subject><subject>Dynamics of the ocean (upper and deep oceans)</subject><subject>Earth, ocean, space</subject><subject>estimation</subject><subject>Exact sciences and technology</subject><subject>External geophysics</subject><subject>Fluid dynamics</subject><subject>Fluid flow</subject><subject>Fluids</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>General theory</subject><subject>Horizontal</subject><subject>Kernel</subject><subject>Laws</subject><subject>Lie group</subject><subject>Memory organisation. Data processing</subject><subject>Noise robustness</subject><subject>Nonlinear equations</subject><subject>observer</subject><subject>Observers</subject><subject>oceanography</subject><subject>Oceans</subject><subject>Physics</subject><subject>Physics of the oceans</subject><subject>Sea measurements</subject><subject>Sea surface</subject><subject>shallow water model</subject><subject>Software</subject><subject>Steady-state</subject><subject>symmetries</subject><subject>wave equation</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkMtLw0AQxhdRsD7ugpcgCHqI7juzx1p8QUHBisdlkk4wmjS62xb637ulpQdPwzfzm-Gbj7EzwW-E4O52MhzdSJ6U5LaQTuyxgTAGcmmk2mcDzgXkToI9ZEcxfiVptRYDZt5WXUfzsMrvMNI0eykjhSWFmNV9yN76jrIPnFPIJzj7zl5DX7bUxRN2UGMb6XRbj9n7w_1k9JSPXx6fR8NxXiko5rkVFiQVprSu0Ci5AYVaq1LBFKfOkgGJRIUrK1Frayy3U2Ug-S-Aa4Oojtn15u4ntv4nNB2Gle-x8U_DsV_3OHfccKGWIrFXG_Yn9L8LinPfNbGitsUZ9YvohS2EEoYDJPTiH_rVL8IsfeIh2QADTieIb6Aq9DEGqncGBPfryH2K3K8j99vI08rl9i7GCts64Kxq4m5PagHOSZe48w3XENFubIx2YJT6A0_ZhUc</recordid><startdate>20110501</startdate><enddate>20110501</enddate><creator>Auroux, D</creator><creator>Bonnabel, S</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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The fluid motion is described by shallow water equations in two horizontal dimensions. We build a simple nonlinear 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.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TAC.2010.2067291</doi><tpages>13</tpages><orcidid>https://orcid.org/0000-0002-8837-2807</orcidid><orcidid>https://orcid.org/0000-0002-6001-7766</orcidid></addata></record> |
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| subjects | Applied sciences Computational fluid dynamics Computer science control theory systems Construction Convergence Convergence of numerical methods Current measurement Data assimilation Data processing. List processing. Character string processing Dynamics of the ocean (upper and deep oceans) Earth, ocean, space estimation Exact sciences and technology External geophysics Fluid dynamics Fluid flow Fluids Fundamental areas of phenomenology (including applications) General theory Horizontal Kernel Laws Lie group Memory organisation. Data processing Noise robustness Nonlinear equations observer Observers oceanography Oceans Physics Physics of the oceans Sea measurements Sea surface shallow water model Software Steady-state symmetries wave equation |
| title | Symmetry-Based Observers for Some Water-Tank Problems |
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