Uncertainty Propagation in Related Control Systems Via the Liouville Equation

Authors

Patricia Mellodge, University of HartfordFollow
Pushkin Kachroo, University of Nevada, Las VegasFollow

Document Type

Article

Publication Date

2010

Publication Title

International Journal of Modelling, Identification and Control

Volume

9

Issue

4

First page number:

392

Last page number:

399

Abstract

This paper studies the relationship between the evolutions of uncertain initial conditions in Φ-related control systems. It is shown that a control system abstraction can capture the time evolution of the uncertainty in the original system by an appropriate choice of control input. Φ-related control systems with stochastic initial conditions show the same behaviour as systems with deterministic initial conditions. A conservation law is applied to the probability density function (pdf) requiring that the area under it be unity. Application of the conservation law results in a partial differential equation known as the Liouville equation, for which a closed form solution is known. The solution provides the time evolution of the initial pdf which can be followed by the abstracted system.

Keywords

Digital control systems; Sturm-Liouville equation; Uncertainty

Disciplines

Controls and Control Theory | Electrical and Computer Engineering | Engineering | Systems and Communications

Language

English

Permissions

Use Find in Your Library, contact the author, or interlibrary loan to garner a copy of the item. Publisher policy does not allow archiving the final published version. If a post-print (author's peer-reviewed manuscript) is allowed and available, or publisher policy changes, the item will be deposited.

Repository Citation

Mellodge, P., Kachroo, P. (2010). Uncertainty Propagation in Related Control Systems Via the Liouville Equation. International Journal of Modelling, Identification and Control, 9(4), 392-399.