Uncertainty propagation in abstracted systems via the Liouville equation / Patricia Mellodge in Transactions of the ASME . Journal of dynamic systems, measurement, and control, Vol. 132 N° 4 (Juillet 2010)  

Public ISBD [article]  inTransactions of the ASME . Journal of dynamic systems, measurement, and control > Vol. 132 N° 4 (Juillet 2010) . - 04 p. Titre : Uncertainty propagation in abstracted systems via the Liouville equation Type de document : texte imprimé Auteurs : Patricia Mellodge, Auteur ; Kachroo, Pushkin, Auteur Année de publication : 2010 Article en page(s) : 04 p. Note générale : Systèmes dynamiques Langues : Anglais (eng) Mots-clés : Dynamics Liouville equation Mechanical engineering Uncertain systems Index. décimale : 629.8 Résumé : This technical brief shows that given a system and its abstraction, the evolution of uncertain initial conditions in the original system is, in some sense, matched by the evolution of the uncertainty in the abstracted system. In other words, it is shown that the concept of Phi-related vector fields extends to the case of stochastic initial conditions where the probability density function (pdf) for the initial conditions is known. In the deterministic case, the Phi mapping commutes with the system dynamics. In this paper, we show that in the case of stochastic initial conditions, the induced mapping Phipdf commutes with the evolution of the pdf according to the Liouville equation. DEWEY : 629.8 ISSN : 0022-0434 En ligne : http://asmedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JDSMAA00013200 [...] [article] Uncertainty propagation in abstracted systems via the Liouville equation [texte imprimé] / Patricia Mellodge, Auteur ; Kachroo, Pushkin, Auteur . - 2010 . - 04 p. Systèmes dynamiques Langues : Anglais (eng) in Transactions of the ASME . Journal of dynamic systems, measurement, and control > Vol. 132 N° 4 (Juillet 2010) . - 04 p. Mots-clés : Dynamics Liouville equation Mechanical engineering Uncertain systems Index. décimale : 629.8 Résumé : This technical brief shows that given a system and its abstraction, the evolution of uncertain initial conditions in the original system is, in some sense, matched by the evolution of the uncertainty in the abstracted system. In other words, it is shown that the concept of Phi-related vector fields extends to the case of stochastic initial conditions where the probability density function (pdf) for the initial conditions is known. In the deterministic case, the Phi mapping commutes with the system dynamics. In this paper, we show that in the case of stochastic initial conditions, the induced mapping Phipdf commutes with the evolution of the pdf according to the Liouville equation. DEWEY : 629.8 ISSN : 0022-0434 En ligne : http://asmedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JDSMAA00013200 [...]

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