Uncertainty Propagation in Related Control Systems Via the Liouville Equation
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.