Title: Uncertainty propagation in Φ related control systems via the Liouville equation

Authors: Patricia Mellodge, Pushkin Kachroo

Addresses: Electrical and Computer Engineering, University of Hartford, West Hartford, Connecticut 06117, USA. ' Electrical and Computer Engineering, University of Nevada Las Vegas, Las Vegas, Nevada 89154, USA

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: abstraction; control systems; Liouville equation; stochastic initial conditions; phi-related control systems; probability density function; uncertainty propagation; commutative relationship; continuity equation; partial differential equations.

DOI: 10.1504/IJMIC.2010.033214

International Journal of Modelling, Identification and Control, 2010 Vol.9 No.4, pp.392 - 399

Published online: 13 May 2010 *

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