Conference proceeding
Worst-case properties of the uniform distribution and randomized algorithms for robustness analysis
PROCEEDINGS OF THE 1997 AMERICAN CONTROL CONFERENCE, VOLS 1-6, pp.861-865
1997
Abstract
Motivated by the current limitations of the existing algorithms for robustness analysis, in this paper we take a different direction which follows the so-called probabilistic approach. That is, we aim to estimate the probability that a control system with uncertain parameters q restricted to a box Q attains a certain level of performance gamma. Since this probability depends on the underlying density function f(q), we study the following question: What is a ''reasonable'' density function so that the estimated probability makes sense? To answer this question, we define two new worst-case criteria and prove that the uniform density function is optimal in both cases. In the second part of the paper, we turn our attention to a subsequent problem. That is, taking f(q) as the uniform density function, we estimate the size of the so-called ''good'' and ''bad'' sets. Roughly speaking, the good set contains the parameters q is an element of Q that have performance level better than or equal to gamma while the bad set is the set of parameters q is an element of Q that have performance level worse than gamma. To estimate the size of both sets, sampling is required. Then, we give bounds on the minimum sample size to attain a given accuracy and confidence.
Details
- Title: Subtitle
- Worst-case properties of the uniform distribution and randomized algorithms for robustness analysis
- Creators
- E W BaiR TempoM FuAMER AUTOMAT CONTROL COUNCIL
- Resource Type
- Conference proceeding
- Publication Details
- PROCEEDINGS OF THE 1997 AMERICAN CONTROL CONFERENCE, VOLS 1-6, pp.861-865
- Language
- English
- Date published
- 1997
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984231969202771
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