Symmetry preserving observers for water tank problems: theory and application to an

Silvère Bonnabel

Description

Niveau: Supérieur
Symmetry-preserving observers for water tank problems: theory and application to an oceanography data assimilation example Silvère Bonnabel Co-workers: Didier Auroux. Pierre Rouchon Mines ParisTech Centre de Robotique Mathématiques et Systèmes 29 sept 2009

• linear observers


• gain matrix


• cx ?


• symmetry-preserving observers


• computational cost


• mines paristech


• ∂f ∂x


• centre de robotique

Sujets

• Auroux
• Alfred Bonnabel High School
• Mines ParisTech

Informations

• Publié par: chaeh
• Nombre de lectures: 20
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Symmetry-preservingobserversforwater tankproblems:theoryandapplicationtoan oceanographydataassimilationexample SilvèreBonnabel Co-workers:DidierAuroux.PierreRouchon MinesParisTech CentredeRobotique MathématiquesetSystèmes [e-mail] 29sept2009

Outline Introductionandmotivations Watertanksystems,symmetries,andobserverdesign Applicationtoanoceanographyexemple Numericalsimulations Conclusion

Symmetrieshavebeenusedincontrolforfeedbackdesignfor non-linearsystemsbutmuchlessforthedesignofnon-linear observerstoourknowledge. Incontroltheory,astateobserverisasystemthatuses I amodeloftherealsystem I noisymeasurementsoftheinputandoutputofthereal system I Goal:provideareal-timeestimateoftheinternalstate Itistypicallyacomputer-implementedmathematicalmodel (preferablylowcostofcomputation).Exemple:Kalmanfilter

Linearobservers Considerthelinearsystem d d t x=Ax+Bu,yxC= wherex ∈ R n isthestate,u ∈ R m theinput,andy ∈ R p the output;A ∈ R n × n ,B ∈ R n × m ,andC ∈ R p × n . LuenbergerObserverorKalmanfilter d d t x ˆ = Ax ˆ + Bu + L ( Cx ˆ −y ) Copy+correctiontermL(Cx ˆ − y)equalto0whenx ˆ =x. Listhegainmatrix