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Optimal Estimation Theory for Dynamic Systems with Set Membership Uncertainty: An Overview

  • Chapter
Bounding Approaches to System Identification

Abstract

In many problems, such as linear and nonlinear regressions, parameter and state estimation of dynamic systems, state space and time series prediction, interpolation, smoothing, and functions approximation, one has to evaluate some unknown variable using available data. The data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables. Typically, the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory. An interesting alternative, referred to as set membership or unknown but bounded (UBB) error description, has been investigated since the late 60s. In this approach, uncertainty is described by an additive noise which is known only to have given integral (typically l 1 or l 2) or componentwise (l ∞) bounds. In this chapter the main results of this theory are reviewed, with special attention to the most recent advances obtained in the case of componentwise bounds.

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Author information

Authors and Affiliations

  1. Dipartimento di Automatica e Informatica, Politecnico di Torino, 10129, Torino, Italy

    M. Milanese

  2. Facoltà di Ingegneria, Università degli Studi di Siena, 53100, Siena, Italy

    A. Vicino

Authors
  1. M. Milanese
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  2. A. Vicino
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Editor information

Editors and Affiliations

  1. Dipartimento di Automatica e Informatica, Politecnico di Torino, Torino, 10129, Italy

    Mario Milanese

  2. School of Electronic and Electrical Engineering, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK

    John Norton

  3. Direction des Études de Synthèse, SM Office National d’Études et de Recherches Aérospatiales, Châtillon Cedex, F-92322, France

    Hélène Piet-Lahanier

  4. Laboratoire des Signaux et Systèmes, CNRS-École Supérieure d’Électricité, Gif-sur-Yvette Cedex, 91192, France

    Éric Walter

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Milanese, M., Vicino, A. (1996). Optimal Estimation Theory for Dynamic Systems with Set Membership Uncertainty: An Overview. In: Milanese, M., Norton, J., Piet-Lahanier, H., Walter, É. (eds) Bounding Approaches to System Identification. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9545-5_2

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  • DOI: https://doi.org/10.1007/978-1-4757-9545-5_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9547-9

  • Online ISBN: 978-1-4757-9545-5

  • eBook Packages: Springer Book Archive

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