Probabilistic robustness analysis: Explicit bounds for the minimum number of samples

R Tempo; E W Bai; F Dabbene

doi:10.1109/CDC.1996.573690

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Conference proceeding

Probabilistic robustness analysis: Explicit bounds for the minimum number of samples

R Tempo, E W Bai and F Dabbene

PROCEEDINGS OF THE 35TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, pp.3424-3428

1996

DOI: 10.1109/CDC.1996.573690

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Abstract

In this paper, we study robustness analysis of control systems affected by bounded uncertainty. Motivated by the difficulty to perform this analysis when the uncertainty enters into the plant coefficients in a nonlinear fashion, we study a probabilistic approach. In this setting, the uncertain parameters q are random variables bounded in a set Q and described by a multivariate density function f(q). We then ask the following question: Given a performance level, what is the probability that this level is attained? The main content of this paper is to derive explicit bounds for the number of samples required to estimate this probability with a certain accuracy and confidence apriori specified. It is shown that the number obtained is inversely proportional to these thresholds and it is much smaller than that of classical results. Finally, we remark that the same approach can be used to study several problems in a control system context. For example, we can evaluate the worst-case H-infinity norm of the sensitivity function or compute mu when the robustness margin is of concern.

Details

Title: Subtitle: Probabilistic robustness analysis: Explicit bounds for the minimum number of samples
Creators: R Tempo
E W Bai
F Dabbene
Resource Type: Conference proceeding
Publication Details: PROCEEDINGS OF THE 35TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, pp.3424-3428
DOI: 10.1109/CDC.1996.573690
Language: English
Date published: 1996
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984231968602771

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