Semiglobal stabilization of a class of nonlinear systems using output feedback

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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“…T to be a global diffeomorphism, in addition to satisfying (2) for all ζ ∈ R n , it also requires condition [24], [12] …”

Section: B Problem Statementmentioning

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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“…We start the observer design by creating a modified high-gain observer according to (3). We then obtain error dynamics of the form (4):…”

Section: A Observer Designmentioning

confidence: 99%

“…Many of the results on high-gain observer design for nonlinear systems, for example [3], [4], rely on placing the system in some variation of the normal form, where it is represented as a chain of integrators from the nonlinearities to the outputs, possibly with a separate subsystem representing the zero dynamics. An alternative to the normal form is the special coordinate basis (SCB) introduced in [5], where the system is divided into subsystems that reflect its zero structure and invertibility properties.…”

Section: Introductionmentioning

confidence: 99%

State and parameter estimation for linear systems with nonlinearly parameterized perturbations

Grip

Saberi

Johansen

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-We consider systems that can be described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. Under a set of technical assumptions about the perturbation and its relationship to the outputs, we present a modular observer design technique. The observers produced by this design technique consist of a modified high-gain observer that estimates the states of the system together with the full perturbation, and a parameter estimator. The parameter estimator is constructed by the designer to identify the unknown parameters by dynamically inverting a nonlinear equation. We illustrate the design technique by constructing an observer for a DC motor with friction modeled by the dynamic LuGre friction model.

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“…Following (Khalil and Esfandiari, 1993) the idea is to implement the controller (15) by substituting the term v = −kẽ with the saturated estimate…”

Section: From Partial State To Pure Error Feedbackmentioning

confidence: 99%

Further Results on Output Regulation by Pure Error Feedback

Byrnes

Isidori

Marconi

2005

IFAC Proceedings Volumes

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This work addresses the design of internal model-based regulators for nonlinear systems by error feedback in the general "non-equilibrium" framework proposed in (Byrnes and Isidori, 2003). The material presented here is specifically meant to complement the work in (Byrnes and Isidori, 2004) where a procedure for designing nonlinear internal model-based regulators was presented for systems having relative degree 1.

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Semiglobal stabilization of a class of nonlinear systems using output feedback

Cited by 281 publications

References 13 publications

On the Output Transformation to an Observer Form

On the Output Transformation to an Observer Form

State and parameter estimation for linear systems with nonlinearly parameterized perturbations

Further Results on Output Regulation by Pure Error Feedback

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