Nonlinear Observer Design by Observer Error Linearization

Xia, Xiaohua; Gao, Wei-Bing

doi:10.1137/0327011

Cited by 373 publications

(189 citation statements)

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“…For linear dynamical systems a complete solution to the problem is well known [13], [14]. For nonlinear systems a few partial results exist [15], [16], [26]- [28]. This observation is at the core of the paper.…”

mentioning

confidence: 80%

An observer looks at synchronization

Nijmeijer

Mareels

1997

IEEE Trans. Circuits Syst. I

628

318

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mentioning

confidence: 80%

An observer looks at synchronization

Nijmeijer

Mareels

1997

IEEE Trans. Circuits Syst. I

628

318

View full text Add to dashboard Cite

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“…The following proof therefore only shows the necessity of these additional conditions. For the proof of the rest conditions, readers are referred to [25], [20].…”

Section: Existence Conditionsmentioning

confidence: 99%

“…The well-established exact error linearization nonlinear observer design method uses an Observer Form (OF) to obtain stable Linear Time-Invariant (LTI) state estimate error dynamics in OF coordinates [14], [2]. Significant effort has been placed on extending this original work for single-output continuous-time systems [15], [25], [7], [23], [18], [11], [13], [19], [16], [3]. Some of the extensions are achieved by eliminating constraints in the target normal forms.…”

Section: Introductionmentioning

confidence: 99%

On the Output Transformation to an Observer Form

Wang

Lynch

Bortoff³

2010

IASTED Technology Conferences / 696:MS / 697:CA / 698: WC / 699: EME / 700: SOE

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This paper investigates the transformability of an unforced multi-output nonlinear system to a multi-output observer form. The existence conditions of an output transformation and a change of state coordinates are presented in a more concise form than those given in literatures. Given an output transformation, verifying these conditions can reveal if the unforced system is transformable to the observer form. Necessary conditions on the output transformation are given for the single output and multi-output nonlinear systems. These necessary conditions are stated as a set of first order partial differential equations, which are relatively easy to solve and potentially useful to obtain the output transformation candidates. The 12th IASTED International Conference on Control and ApplicationsThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. MERLCoverPageSide2On the output transformation to an observer form Yebin Wang, Alan F. Lynch, and Scott A. BortoffAbstract-This paper investigates the transformability of an unforced multi-output nonlinear system to a multi-output observer form. The existence conditions of an output transformation and a change of state coordinates are presented in a more concise form than those given in literatures. Given an output transformation, verifying these conditions can reveal if the unforced system is transformable to the observer form. Necessary conditions on the output transformation are given for the single output and multi-output nonlinear systems. These necessary conditions are stated as a set of first order partial differential equations, which are relatively easy to solve and potentially useful to otain the output transformation candidates.

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“…The first attempts towards nonlinear observer design were to identify necessary and sufficient conditions on a nonlinear system for converting it into a simpler form like a linear or a bilinear system up to an output injection term, for which an observer can be easily constructed (Besancon, 1999;Hammouri & Gauthier, 1989;Krener & Respondek, 1985;Levine & Marino, 1986;Xia & Gao, 1989). See also Shim, Seo, and Teel (2003) and the references in there.…”

Section: Introductionmentioning

confidence: 99%

Full-order observer design for a class of port-Hamiltonian systems

Venkatraman

Schaft

2010

Automatica

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a b s t r a c tWe consider a special class of port-Hamiltonian systems for which we propose a design methodology for constructing globally exponentially stable full-order observers using a passivity based approach. The essential idea is to make the augmented system consisting of the plant and the observer dynamics to become strictly passive with respect to an invariant manifold defined on the extended state-space, on which the state estimation error is zero. We first introduce the concept of passivity of a system with respect to a manifold by defining a new input and output on the extended state-space and then perform a partial state feedback passivation which leads to the construction of the observer. We then illustrate this observer design procedure on two physical examples, the magnetic levitation system and the inverted pendulum on the cart system.

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Nonlinear Observer Design by Observer Error Linearization

Cited by 373 publications

References 6 publications

An observer looks at synchronization

An observer looks at synchronization

On the Output Transformation to an Observer Form

Full-order observer design for a class of port-Hamiltonian systems

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