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Bounding Approaches to System Identification pp 119–138Cite as

Volume-Optimal Inner and Outer Ellipsoids

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Abstract

Approximating a complex set K by a simple geometrical form (such as a polytope, an orthotope, a sphere or an ellipsoid) is often of practical interest. Consider for instance the situation where a vector u has to be chosen so as to satisfy the property

$$ p\left( {u,x} \right) \in T,\forall x \in S, $$
((8.1))

where x and p(.,.) are vector-valued and where T and S are given sets. This can be of interest for instance in robust control, where the controller characterized by u must be designed in order to guarantee some given performances—at least stability—corresponding to a target set T for the process under study, given the information that the model parameters x lie in some specified feasible domain S. The information about S can be derived using the parameter bounding methodology, where one assumes that observations with bounded errors are performed on the process.(1)

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Author information

Authors and Affiliations

  1. Laboratoire 13S, CNRS URA-1376, Sophia Antipolis, 06560, Valbonne, France

    L. Pronzato

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

    É. Walter

Authors
  1. L. Pronzato
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  2. É. Walter
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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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© 1996 Springer Science+Business Media New York

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Pronzato, L., Walter, É. (1996). Volume-Optimal Inner and Outer Ellipsoids. 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_8

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  • DOI: https://doi.org/10.1007/978-1-4757-9545-5_8

  • 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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