Chance-constrained sets approximation: A probabilistic scaling approach

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 scales these sets to obtain the desired probabilistic guarantees. The proposed approach is shown to be applicable in several problems in systems and control, such as the design of Stochastic Model Predictive Control schemes or the solution of probabilistic set membership estimation problems.