Model reduction for nonlinear systems with incremental gain or passivity properties

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Abstract

In this paper, model reduction techniques for a class of nonlinear systems are proposed. Specifically, nonlinear systems are considered that can be decomposed as the feedback interconnection of a high-order linear subsystem and a nonlinear subsystem of relatively low order, allowing for the application of well-developed reduction techniques for linear systems. In this setting, conditions are given under which internal stability, as well as passivity or a bound on the L2 gain are preserved for the reduced-order nonlinear model. Additionally, a priori error bounds are given. In the derivation of the error bound, an incremental gain (or incremental passivity) property of the nonlinear subsystem is shown to be instrumental. Additionally, the techniques developed in this paper are applied in the scope of controller reduction, as is illustrated by means of an industrial temperature control benchmark example.
Original languageEnglish
Pages (from-to)861-872
Number of pages12
JournalAutomatica
Volume494
Issue number4
DOIs
Publication statusPublished - 2013

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Nonlinear systems
Temperature control
Linear systems
Feedback
Controllers

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title = "Model reduction for nonlinear systems with incremental gain or passivity properties",
abstract = "In this paper, model reduction techniques for a class of nonlinear systems are proposed. Specifically, nonlinear systems are considered that can be decomposed as the feedback interconnection of a high-order linear subsystem and a nonlinear subsystem of relatively low order, allowing for the application of well-developed reduction techniques for linear systems. In this setting, conditions are given under which internal stability, as well as passivity or a bound on the L2 gain are preserved for the reduced-order nonlinear model. Additionally, a priori error bounds are given. In the derivation of the error bound, an incremental gain (or incremental passivity) property of the nonlinear subsystem is shown to be instrumental. Additionally, the techniques developed in this paper are applied in the scope of controller reduction, as is illustrated by means of an industrial temperature control benchmark example.",
author = "B. Besselink and {Wouw, van de}, N. and H. Nijmeijer",
year = "2013",
doi = "10.1016/j.automatica.2013.01.004",
language = "English",
volume = "494",
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journal = "Automatica",
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publisher = "Agon Elsevier",
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Model reduction for nonlinear systems with incremental gain or passivity properties. / Besselink, B.; Wouw, van de, N.; Nijmeijer, H.

In: Automatica, Vol. 494, No. 4, 2013, p. 861-872.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Model reduction for nonlinear systems with incremental gain or passivity properties

AU - Besselink, B.

AU - Wouw, van de, N.

AU - Nijmeijer, H.

PY - 2013

Y1 - 2013

N2 - In this paper, model reduction techniques for a class of nonlinear systems are proposed. Specifically, nonlinear systems are considered that can be decomposed as the feedback interconnection of a high-order linear subsystem and a nonlinear subsystem of relatively low order, allowing for the application of well-developed reduction techniques for linear systems. In this setting, conditions are given under which internal stability, as well as passivity or a bound on the L2 gain are preserved for the reduced-order nonlinear model. Additionally, a priori error bounds are given. In the derivation of the error bound, an incremental gain (or incremental passivity) property of the nonlinear subsystem is shown to be instrumental. Additionally, the techniques developed in this paper are applied in the scope of controller reduction, as is illustrated by means of an industrial temperature control benchmark example.

AB - In this paper, model reduction techniques for a class of nonlinear systems are proposed. Specifically, nonlinear systems are considered that can be decomposed as the feedback interconnection of a high-order linear subsystem and a nonlinear subsystem of relatively low order, allowing for the application of well-developed reduction techniques for linear systems. In this setting, conditions are given under which internal stability, as well as passivity or a bound on the L2 gain are preserved for the reduced-order nonlinear model. Additionally, a priori error bounds are given. In the derivation of the error bound, an incremental gain (or incremental passivity) property of the nonlinear subsystem is shown to be instrumental. Additionally, the techniques developed in this paper are applied in the scope of controller reduction, as is illustrated by means of an industrial temperature control benchmark example.

U2 - 10.1016/j.automatica.2013.01.004

DO - 10.1016/j.automatica.2013.01.004

M3 - Article

VL - 494

SP - 861

EP - 872

JO - Automatica

JF - Automatica

SN - 0005-1098

IS - 4

ER -