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Motivation and Problem Statement

  • Pauline BernardEmail author
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 479)

Abstract

The previous two parts have shown that the observer design usually consists in transforming the system into a favorable form for which a global observer is known. It follows that the plant’s and observer’s dynamics are not expressed in the same coordinates and may not have the same dimensions: in order to obtain an estimate of the plant’s state, it is therefore necessary to inverse the transformation. When no explicit expression for a global inverse is available, numerical inversion usually relies on the resolution of a minimization problem with a heavy computational cost. Other methods rely on gradient/Newton algorithms which provide only local convergence. In Part III, a recently developed method is presented, whose goal is to bring the observer dynamics (expressed in the normal form coordinates) back into the initial plant’s coordinates. In the case where the transformation is a stationary injective immersion, a first sufficient condition is given, namely that the transformation can be extended into a surjective diffeomorphism.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi”University of BolognaBolognaItaly

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