Uncertainty Propagation in Abstracted Systems Via the Liouville Equation

Document Type

Article

Publication Date

6-17-2010

Publication Title

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Volume

132

Issue

4

First page number:

1

Last page number:

4

Abstract

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 Φ-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 Φ mapping commutes with the system dynamics. In this paper, we show that in the case of stochastic initial conditions, the induced mapping Φpdf commutes with the evolution of the pdf according to the Liouville equation.

Keywords

Liouville equation; Probability; Uncertainty

Disciplines

Electrical and Computer Engineering | Engineering | Systems and Communications

Language

English

Permissions

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