Model Reduction for Nonlinear Systems by Incremental Balanced Truncation

Bart Besselink*, Nathan van de Wouw, Jacquelien M. A. Scherpen, Henk Nijmeijer

*Bijbehorende auteur voor dit werk

OnderzoeksoutputAcademicpeer review

37 Citaten (Scopus)

Samenvatting

In this paper, the method of incremental balanced truncation is introduced as a tool for model reduction of nonlinear systems. Incremental balanced truncation provides an extension of balanced truncation for linear systems towards the nonlinear case and differs from existing nonlinear balancing techniques in the definition of two novel energy functions. These incremental observability and incremental controllability functions form the basis for a model reduction procedure in which the preservation of stability properties is guaranteed. In particular, the property of incremental stability, which provides a notion of stability for systems with nonzero inputs, is preserved. Moreover, a computable error bound is given. Next, an extension towards so-called generalized incremental balanced truncation is proposed, which provides a reduction technique with increased computational feasibility at the cost of a (potentially) larger error bound. The proposed reduction technique is illustrated by means of application to an example of an electronic circuit with nonlinear elements.

Originele taal-2English
Pagina's (van-tot)2739-2753
Aantal pagina's15
TijdschriftIEEE Transactions on Automatic Control
Volume59
Nummer van het tijdschrift10
DOI's
StatusPublished - 2014

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