  In this paper, a sample-based procedure for obtaining simple and computable
approximations of chance-constrained sets is proposed. The procedure allows to
control the complexity of the approximating set, by defining families of
simple-approximating sets of given complexity. A probabilistic scaling
procedure then allows to rescale these sets to obtain the desired probabilistic
guarantees. The proposed approach is shown to be applicable in several problem
in systems and control, such as the design of Stochastic Model Predictive
Control schemes or the solution of probabilistic set membership estimation
problems.
