 
Summary: Applications of StatisticalLearning Control in Systems and
Control
M. Ariola # , C. T. Abdallah + , V. Koltchinskii #
March 21, 2003
IFAC Workshop on Adaptation and Learning in Control and Signal Processing
August 2931, 2001, Villa Erba, CernobbioComo (ITALY)
Extended abstract
It has been recently shown that many control problems are too di#cult to admit analytic solutions [2,
3]. These controls problems include fixedorder controller design [11], robust multiobjective control [1],
hybrid systems control [10], timedelay systems [9], and others [5]. Even though such questions may
be too di#cult to answer analytically, or may not be answerable exactly given a reasonable amount of
computational resources, researchers have shown that we can ``approximately'' answer these questions
``most of the time'', and have ``high confidence'' in the correctness of the answers. This is the gist of the
probabilistic methods, which many authors have recently proposed in control analysis and design. These
methods build on the standard Monte Carlo approach (with justifications based on Cherno# Bounds,
Hoe#ding Inequality, and other elementary probabilistic tools [14]) with ideas advanced during the 1960s
and on the theory of empirical processes and statistical learning developed in the 1970s and 1980s. In
control theory, some of the original (Monte Carlo) ideas have already been used in [12, 6] to solve robust
analysis problems while Vidyasagar [15] and the authors [8] used learning theory to solve robust design
problems. The basic idea of using learning methods in such problems is to convert a highly complex
