  For discrete-time linear systems subject to parametric uncertainty described
by random variables, we develop a sampling-based Stochastic Model Predictive
Control algorithm. Unlike earlier results employing a scenario approximation,
we propose an offline sampling approach in the design phase instead of online
scenario generation. The paper highlights the structural difference between
online and offline sampling and provides rigorous bounds on the number of
samples needed to guarantee chance constraint satisfaction. The approach does
not only significantly speed up the online computation, but furthermore allows
to suitably tighten the constraints to guarantee robust recursive feasibility
when bounds on the uncertain variables are provided. Under mild assumptions,
asymptotic stability of the origin can be established.
