Improved sample size bounds for probabilistic robust control design: A pack-based strategy

This paper deals with probabilistic methods and randomized algorithms for robust control design. The main contribution is to introduce a new technique, denoted as "pack- based strategy". When combined with recent results available in the literature, this technique leads to significant improvements in terms of sample size reduction. One of the main results is to show that for fixed confidence delta, the required sample size increases as 1/isin, where isin denotes the guaranteed accuracy. Using this technique for non-convex optimization problems involving Boolean expressions consisting of polynomials, we prove that the number of required samples grows with the accuracy parameter isin as 1/isin In 1/isin.