Journal ArticleDOI
Statistical learning theory and randomized algorithms for control
TLDR
The use of randomized algorithms to solve some problems in control system designs that are perceived to be "difficult" is presented to show that the randomized approach can be quite successful in tackling a practical problem.Abstract:
The topic of the present article is the use of randomized algorithms to solve some problems in control system designs that are perceived to be "difficult". A brief introduction is given to the notions of computational complexity that are pertinent to the present discussion, and then some problems in control system analysis and synthesis that are difficult in a complexity-theoretic sense are described. Some of the elements of statistical learning theory, which forms the basis of the randomized approach, are briefly described. Finally, these two sets of ideas are brought together to show that it is possible to construct efficient randomized algorithms for each of the difficult problems discussed by using the ideas of statistical learning theory. A real-life design example of synthesizing a first-order controller for the longitudinal stabilization of an unstable fighter aircraft is then presented to show that the randomized approach can be quite successful in tackling a practical problem.read more
Citations
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Book
Stability of Time-Delay Systems
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Recursive Bayesian Estimation : Navigation and Tracking Applications
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Journal ArticleDOI
Randomized Strategies for Probabilistic Solutions of Uncertain Feasibility and Optimization Problems
TL;DR: A randomized algorithm is proposed that provides a probabilistic solution circumventing the potential conservatism of the bounds previously derived, and it is proved that the required sample size is inversely proportional to the accuracy for fixed confidence.
Journal ArticleDOI
Survey paper: Research on probabilistic methods for control system design
TL;DR: In this paper, the authors provide a broad perspective on this area of research known as ''probabilistic robust control'' and to address in a systematic manner recent advances, focusing on design methods based on the interplay between uncertainty randomization and convex optimization, and on the illustration of specific control applications.
Research on probabilistic methods for control system design. Automatica
TL;DR: The main objective of this paper is to provide a broad perspective on this area of research known as ''probabilistic robust control'', and to address in a systematic manner recent advances.
References
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Book ChapterDOI
Probability Inequalities for sums of Bounded Random Variables
TL;DR: In this article, upper bounds for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt are derived for certain sums of dependent random variables such as U statistics.
Proceedings ArticleDOI
The complexity of theorem-proving procedures
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A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
TL;DR: In this paper, it was shown that the likelihood ratio test for fixed sample size can be reduced to this form, and that for large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample with the second test.
Analysis of feedback systems with structured uncertainties
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