  Handling uncertainty in model predictive control comes with various
challenges, especially when considering state constraints under uncertainty.
Most methods focus on either the conservative approach of robustly accounting
for uncertainty or allowing a small probability of constraint violation. In
this work, we propose a linear model predictive control approach that minimizes
the probability that linear state constraints are violated in the presence of
additive uncertainty. This is achieved by first determining a set of inputs
that minimize the probability of constraint violation. Then, this resulting set
is used to define admissible inputs for the optimal control problem. Recursive
feasibility is guaranteed and input-to-state stability is proved under
assumptions. Numerical results illustrate the benefits of the proposed model
predictive control approach.
