  This work presents DMPC (Data-and Model-Driven Predictive Control) to solve
control problems in which some of the constraints or parts of the objective
function are known, while others are entirely unknown to the controller. It is
assumed that there is an exogenous ``black box'' system, e.g. a machine
learning technique, that predicts the value of the unknown functions for a
given trajectory. DMPC (1) provides an approach to merge both the model-based
and black-box systems; (2) can cope with very little data and is sample
efficient, building its solutions based on recently generated trajectories; and
(3) improves its cost in each iteration until converging to an optimal
trajectory, typically needing only a few trials even for nonlinear dynamics and
objectives. Theoretical analysis of the algorithm is presented, proving that
the quality of the trajectory does not worsen with each new iteration, as well
as providing bounds on the complexity. We apply the DMPC algorithm to the
motion planning of an autonomous vehicle with nonlinear dynamics.
