  While it has been repeatedly shown that learning-based controllers can
provide superior performance, they often lack of safety guarantees. This paper
aims at addressing this problem by introducing a model predictive safety
certification (MPSC) scheme for polytopic linear systems with additive
disturbances. The scheme verifies safety of a proposed learning-based input and
modifies it as little as necessary in order to keep the system within a given
set of constraints. Safety is thereby related to the existence of a model
predictive controller (MPC) providing a feasible trajectory towards a safe
target set. A robust MPC formulation accounts for the fact that the model is
generally uncertain in the context of learning, which allows proving constraint
satisfaction at all times under the proposed MPSC strategy. The MPSC scheme can
be used in order to expand any potentially conservative set of safe states for
learning and we prove an iterative technique for enlarging the safe set.
Finally, a practical data-based design procedure for MPSC is proposed using
scenario optimization.
