  While Robust Model Predictive Control considers the worst-case system
uncertainty, Stochastic Model Predictive Control, using chance constraints,
provides less conservative solutions by allowing a certain constraint violation
probability depending on a predefined risk parameter. However, for
safety-critical systems it is not only important to bound the constraint
violation probability but to reduce this probability as much as possible.
Therefore, an approach is necessary that minimizes the constraint violation
probability while ensuring that the Model Predictive Control optimization
problem remains feasible. We propose a novel Model Predictive Control scheme
that yields a solution with minimal constraint violation probability for a norm
constraint in an environment with uncertainty. After minimal constraint
violation is guaranteed the solution is then also optimized with respect to
other control objectives. Further, it is possible to account for changes over
time of the support of the uncertainty. We first present a general method and
then provide an approach for uncertainties with symmetric, unimodal probability
density function. Recursive feasibility and convergence of the method are
proved. A simulation example demonstrates the effectiveness of the proposed
method.
