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What is Ellipsoidal Modelling and How to Use It for Control and State Estimation?

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Whys and Hows in Uncertainty Modelling

Part of the book series: CISM Courses and Lectures ((CISM,volume 388))

Abstract

The paper is devoted to the overview of the method of ellipsoids for modelling and estimating uncertainties in dynamical systems. The method was developed during the last decades and belongs to the guaranteed (minimax or set-membership) approach to description of uncertain factors such as disturbances, measurement errors, indeterminate parameters, etc. By contrast to the well-known probabilistic approach, the guaranteed approach does not require precise knowledge of probability distributions (which are seldom available in practical problems) and yields reliable estimates for the system behavior. Whereas the guaranteed approach operates with the sets of uncertain parameters, the ellipsoidal technique essentially simplifies the estimation procedure by replacing general n-dimensional sets by their inner and outer ellipsoidal estimates. Thus, two-sided optimal estimates are obtained for reachable sets of dynamical systems. The fundamentals of the method of ellipsoids are presented, and the basic properties of the approximating ellipsoids are discussed. Various applications of the method to problems in control and state estimation are given.

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Author information

Authors and Affiliations

  1. Russian Academy of Sciences, Moscow, Russia

    F. L. Chernousko

Authors
  1. F. L. Chernousko
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Editor information

Editors and Affiliations

  1. Florida Atlantic University, USA

    Isaac Elishakoff

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© 1999 Springer-Verlag Wien

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Chernousko, F.L. (1999). What is Ellipsoidal Modelling and How to Use It for Control and State Estimation?. In: Elishakoff, I. (eds) Whys and Hows in Uncertainty Modelling. CISM Courses and Lectures, vol 388. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2501-4_3

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  • DOI: https://doi.org/10.1007/978-3-7091-2501-4_3

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-2503-8

  • Online ISBN: 978-3-7091-2501-4

  • eBook Packages: Springer Book Archive

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