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Probabilistic Robustness Analysis and Design of Uncertain Systems

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Dynamical Systems, Control, Coding, Computer Vision

Part of the book series: Progress in Systems and Control Theory ((PSCT,volume 25))

Abstract

In the probabilistic approach for robustness analysis and design, one of the objectives is to compute the probability that a control system subject to uncertainty Δ, either real, complex or mixed, restricted to a set Δ attains a given performance level γ. Then, it is crucial to derive explicit bounds for the number of samples required to estimate this probability with a certain accuracy and confidence a priori specified. It can be easily shown that the number N of randomly generated samples is independent of the number of blocks of Δ and the size of Δ. This fact is an immediate consequence of the Law of Large Numbers and is often used in Monte Carlo simulation. In the first part of the paper we discuss several bounds and we show their application to probabilistic robustness analysis. Subsequently, we explain how probabilistic robust design can be performed and we discuss connections with Learning Theory, showing how the problem structure can be taken into account. Current research directions related to sample generation in various sets are finally outlined.

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Author information

Authors and Affiliations

  1. Politecnico di Torino, CENS-CNR, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    R. Tempo & F. Dabbene

Authors
  1. R. Tempo
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  2. F. Dabbene
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Editor information

Editors and Affiliations

  1. Dipartimento di Elettronica e Informatica, Università di Padova, vai Gradenigo, 6/A, 35131, Padova, Italia

    Giorgio Picci

  2. Department of Mathematics and Statistics, Texas Tech University, Box 41042, 79409-1042, Lubbock, TX, USA

    David S. Gilliam

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© 1999 Birkhäuser Verlag Basel/Switzerland

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Tempo, R., Dabbene, F. (1999). Probabilistic Robustness Analysis and Design of Uncertain Systems. In: Picci, G., Gilliam, D.S. (eds) Dynamical Systems, Control, Coding, Computer Vision. Progress in Systems and Control Theory, vol 25. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-8970-4_12

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  • DOI: https://doi.org/10.1007/978-3-0348-8970-4_12

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9848-5

  • Online ISBN: 978-3-0348-8970-4

  • eBook Packages: Springer Book Archive

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