On the Representation of Hysteresis Operators of Preisach Type

R. V. Iyer; Robert Paige

doi:10.1016/j.physb.2005.10.012

On the Representation of Hysteresis Operators of Preisach Type

R. V. Iyer
, Robert Paige

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Brokate and Sprekels introduced the notion of hysteresis operators of the Preisach type (HOPTs), that are more general than (and include as a subset) the classical Preisach operator. In this paper, we provide a mathematical framework to the important representation problem for HOPTs by presenting two results on the approximation of the output function on the set of memory curves. One of the results shows the existence of a neural network representation when the functional is continuous, and the other shows a representation based on a multiresolution analysis when the functional is Hölder continuous and bounded on compact subsets of the space of memory curves.

Original language	American English
Journal	Physica B: Condensed Matter
DOIs	https://doi.org/10.1016/j.physb.2005.10.012
State	Published - Jan 1 2006

Keywords

hysteresis operators of Preisach type
multiresolution analysis
neural networks
representation problem

Disciplines

Mathematics
Statistics and Probability

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https://doi.org/10.1016/j.physb.2005.10.012

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title = "On the Representation of Hysteresis Operators of Preisach Type",

abstract = " Brokate and Sprekels introduced the notion of hysteresis operators of the Preisach type (HOPTs), that are more general than (and include as a subset) the classical Preisach operator. In this paper, we provide a mathematical framework to the important representation problem for HOPTs by presenting two results on the approximation of the output function on the set of memory curves. One of the results shows the existence of a neural network representation when the functional is continuous, and the other shows a representation based on a multiresolution analysis when the functional is H{\"o}lder continuous and bounded on compact subsets of the space of memory curves.",

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AU - Paige, Robert

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N2 - Brokate and Sprekels introduced the notion of hysteresis operators of the Preisach type (HOPTs), that are more general than (and include as a subset) the classical Preisach operator. In this paper, we provide a mathematical framework to the important representation problem for HOPTs by presenting two results on the approximation of the output function on the set of memory curves. One of the results shows the existence of a neural network representation when the functional is continuous, and the other shows a representation based on a multiresolution analysis when the functional is Hölder continuous and bounded on compact subsets of the space of memory curves.

AB - Brokate and Sprekels introduced the notion of hysteresis operators of the Preisach type (HOPTs), that are more general than (and include as a subset) the classical Preisach operator. In this paper, we provide a mathematical framework to the important representation problem for HOPTs by presenting two results on the approximation of the output function on the set of memory curves. One of the results shows the existence of a neural network representation when the functional is continuous, and the other shows a representation based on a multiresolution analysis when the functional is Hölder continuous and bounded on compact subsets of the space of memory curves.

KW - hysteresis operators of Preisach type

KW - multiresolution analysis

KW - neural networks

KW - representation problem

UR - https://scholarsmine.mst.edu/math_stat_facwork/298

UR - https://doi.org/10.1016/j.physb.2005.10.012

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DO - 10.1016/j.physb.2005.10.012

M3 - Article

JO - Physica B: Condensed Matter

JF - Physica B: Condensed Matter

ER -

On the Representation of Hysteresis Operators of Preisach Type

Abstract

Keywords

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