Randomized control design through probabilistic validation

In this paper, we present a randomized strategy for design under uncertainty. The main contribution is to provide a general class of sequential algorithms which satisfy the required specifications using probabilistic validation. At each iteration of the sequential algorithm, a candidate solution is probabilistically validated by means of a set of randomly generated uncertainty samples. The idea of validation sets has been used in some randomized algorithms when a given candidate solution is classified as probabilistic solution when it satisfies all the constraints on the validation set. In this paper, we show the limitations of this strategy and present a more general setting where the candidate solution may violate the specifications for a reduced number of elements of the validation set. This generalized scheme exhibits some advantages, in particular in terms of obtaining a probabilistic solution.