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Complexity reduction of Nonlinear Systems

Bian, Wenming and French, Mark (2010) Complexity reduction of Nonlinear Systems At 49th IEEE Conference on Decision and Control, Georgia. 15 - 17 Dec 2010. , pp. 2444-2449.

Record type: Conference or Workshop Item (Paper)

Abstract

A common problem in nonlinear control is the need to consider systems of high complexity. Here we consider systems, which although may be low order, have high complexity due to a complex right hand side of a differential equation (e.g. a right hand side which has many terms – such systems arise from coordinate transformations in constructive nonlinear control designs). This contribution develops a systematic method for the reduction of this complexity, complete with error bounds. In the case when the underling nonlinear system input/output operator is stable and differentiable, the operator Taylor expansion, truncated after a finite number of terms, is taken as the approximation. If the nonlinear system i/o operator is not stable, but admits a coprime factorizations, the Taylor approximation is made to both coprime factors. By bounding the gap between the polynomial system and the original nominal plant, and applying gap robust stability approaches, it is proved that local stability of approximation implies the local stability of the underlining nonlinear systems, and explicit robust stability margins and performance bounds obtained. For systems specified by a finite dimensional first order differential equation, the first order approximant is the system linearisation and the higher order approximants have greater state dimension but with polynomial right hand sides.

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More information

Published date: December 2010
Additional Information: Event Dates: December 15-17, 2010
Venue - Dates: 49th IEEE Conference on Decision and Control, Georgia, 2010-12-15 - 2010-12-17
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 267852
URI: http://eprints.soton.ac.uk/id/eprint/267852
PURE UUID: 48df7b2b-1983-4357-8112-05df9165a144

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Date deposited: 06 May 2011 12:39
Last modified: 18 Jul 2017 06:59

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Contributors

Author: Wenming Bian
Author: Mark French

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