In this paper, we study the sample complexity of probabilistic methods for
uncertain systems. In particular, we show the role of the binomial distribution
for some problems involving analysis and design of robust controllers with
finite families. We also address the particular case in which the design
problem can be formulated as an uncertain convex optimization problem. The
second main contribution of the paper is to study a general class of sequential
algorithms which satisfy the required specifications using probabilistic
validation methods and, at each iteration of the sequential algorithm, a
candidate solution is probabilistically validated. The results of the paper
provide the sample complexity which guarantees that the obtained solutions meet
some pre-specified probabilistic specifications.
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