  Model predictive control (MPC) is an effective approach to control
multivariable dynamic systems with constraints. Most real dynamic models are
however affected by plant-model mismatch and process uncertainties, which can
lead to closed-loop performance deterioration and constraint violations.
Methods such as stochastic MPC (SMPC) have been proposed to alleviate these
problems; however, the resulting closed-loop state trajectory might still
significantly violate the prescribed constraints if the real system deviates
from the assumed disturbance distributions made during the controller design.
In this work we propose a novel data-driven distributionally robust MPC scheme
for nonlinear systems. Unlike SMPC, which requires the exact knowledge of the
disturbance distribution, our scheme decides the control action with respect to
the worst distribution from a distribution ambiguity set. This ambiguity set is
defined as a Wasserstein ball centered at the empirical distribution. Due to
the potential model errors that cause off-sets, the scheme is also extended by
leveraging an offset-free method. The favorable results of this control scheme
are demonstrated and empirically verified with a nonlinear mass spring system
and a nonlinear CSTR case study.
