  Combining efficient and safe control for safety-critical systems is
challenging. Robust methods may be overly conservative, whereas probabilistic
controllers require a trade-off between efficiency and safety. In this work, we
propose a safety algorithm that is compatible with any stochastic Model
Predictive Control method for linear systems with additive uncertainty and
polytopic constraints. This safety algorithm allows to use the optimistic
control inputs of stochastic Model Predictive Control as long as a safe backup
planner can ensure safety with respect to satisfying hard constraints subject
to bounded uncertainty. Besides ensuring safe behavior, the proposed stochastic
Model Predictive Control algorithm guarantees recursive feasibility and
input-to-state stability of the system origin. The benefits of the safe
stochastic Model Predictive Control algorithm are demonstrated in a numerical
simulation, highlighting the advantages compared to purely robust or stochastic
predictive controllers.
