  In Model Predictive Control (MPC), discrepancies between the actual system
and the predictive model can lead to substantial tracking errors and
significantly degrade performance and reliability. While such discrepancies can
be alleviated with more complex models, this often complicates controller
design and implementation. By leveraging the fact that many trajectories of
interest are periodic, we show that perfect tracking is possible when
incorporating a simple observer that estimates and compensates for periodic
disturbances. We present the design of the observer and the accompanying
tracking MPC scheme, proving that their combination achieves zero tracking
error asymptotically, regardless of the complexity of the unmodelled dynamics.
We validate the effectiveness of our method, demonstrating asymptotically
perfect tracking on a high-dimensional soft robot with nearly 10,000 states and
a fivefold reduction in tracking errors compared to a baseline MPC on
small-scale autonomous race car experiments.
