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Optimal Ellipsoidal Estimates of Uncertain Systems: An Overview and New Results

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Coping with Uncertainty

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 633))

Abstract

The method of ellipsoids for the guaranteed state estimation of uncertain dynamical systems is associated with optimal two-sided ellipsoidal bounds for reachable sets of the systems. Being based on the set-membership approach to uncertainties, the method can be regarded as a natural counterpart to well-known stochastic, or probabilistic, techniques. Basic concepts and results of the method are outlined, and certain results are presented. Various possible applications to problems in control, estimation, and observation are considered.

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Acknowledgements

This work was supported by the Russian Foundation for Basic Research (Project 08-01-00411) and by the Grant of Support for Leading Russian Scientific Schools (NSh-4315.2008.1).

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Authors and Affiliations

  1. Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo, 101-1, 119526, Moscow, Russia

    F. L. Chernousko

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  1. F. L. Chernousko
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Correspondence to F. L. Chernousko .

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Editors and Affiliations

  1. Aerospace Engineering and, Technology, Federal Armed Forces University Munich, Werner-Heisenberg-Weg 39, Neubiberg/München, 85577, Germany

    Kurt Marti

  2. Applied Systems Analysis (IIASA), International Institute for, Schloßplatz 1, Laxenburg, 2361, Austria

    Yuri Ermoliev

  3. Applied Systems Analysis (IIASA), International Institute for, Schloßplatz 1, Laxenburg, 2361, Austria

    Marek Makowski

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Chernousko, F.L. (2010). Optimal Ellipsoidal Estimates of Uncertain Systems: An Overview and New Results. In: Marti, K., Ermoliev, Y., Makowski, M. (eds) Coping with Uncertainty. Lecture Notes in Economics and Mathematical Systems, vol 633. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03735-1_7

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