View
Publication Type
Conference Proceedings
UWI Author(s)
Author, Analytic
Kelly, Conall S
Author Role
n/a
Author Affiliation
n/a
Paper/Section Title
Stabilization of Difference Equations with noisy prediction-based control
Medium Designator
n/a
Connective Phrase
n/a
Editor/Compiler
n/a
Editor/Compiler Role
n/a
Proceedings Title
22nd International Conference on Difference Equations and Applications
Date of Meeting
July 24-29, 2016
Place of Meeting
Osaka, Japan
Place of Publication
n/a
Publisher Name
n/a
Date of Publication
n/a
Date of Copyright
n/a
Volume ID
n/a
Location in Work
n/a
Extent of Work
n/a
Packaging Method
n/a
Series Editor
n/a
Series Editor Role
n/a
Series Title
n/a
Series Volume ID
n/a
Location/URL
n/a
ISBN
n/a
Notes
n/a
Abstract
We consider the influence of stochastic perturbations on stability of a unique positive equilibrium of a difference equation subject to prediction-based control. These perturbations may be multiplicative if they arise from stochastic variation of the control parameter, or additive if they reflect the presence of systemic noise. We begin by relaxing the control parameter in the deterministic equation, and deriving a range of values for the parameter over which all solutions eventually enter an invariant interval. Then, by allowing the variation to be stochastic, we derive sufficient conditions (less restrictive than known ones for the unperturbed equation) under which the positive equilibrium will be globally a.s. asymptotically stable: i.e. the presence of noise improves the known effectiveness of prediction-based control. Finally, we show that systemic noise has a “blurring” effect on the positive equilibrium, which can be made arbitrarily small by controlling the noise intensity. Numerical examples illustrate our results.....
read more
Keywords
n/a