  In this paper, we propose a novel model predictive control (MPC) framework
for output tracking that deals with partially unknown constraints. The MPC
scheme optimizes over a learning and a backup trajectory. The learning
trajectory aims to explore unknown and potentially unsafe areas, if and only if
this might lead to a potential performance improvement. On the contrary, the
backup trajectory lies in the known space, and is intended to ensure safety and
convergence. The cost function for the learning trajectory is divided into a
tracking and an offset cost, while the cost function for the backup trajectory
is only marginally considered and only penalizes the offset cost. We show that
the proposed MPC scheme is not only able to safely explore the unknown
constraints, but also escape from local minima that may arise from the presence
of obstacles. Moreover, we provide formal guarantees for convergence and
recursive feasibility of the MPC scheme, as well as closed-loop constraint
satisfaction. Finally, the proposed MPC scheme is demonstrated in simulations
using an example of autonomous vehicle driving in a partially unknown
environment where unknown obstacles are present.
