  Model mismatch and process noise are two frequently occurring phenomena that
can drastically affect the performance of model predictive control (MPC) in
practical applications. We propose a principled way to tune the cost function
and the constraints of linear MPC schemes to achieve good performance and
robust constraint satisfaction on uncertain nonlinear dynamics with additive
noise. The tuning is performed using a novel MPC tuning algorithm based on
backpropagation developed in our earlier work. Using the scenario approach, we
provide probabilistic bounds on the likelihood of closed-loop constraint
violation over a finite horizon. We showcase the effectiveness of the proposed
method on linear and nonlinear simulation examples.
