  We propose a data-driven tracking model predictive control (MPC) scheme to
control unknown discrete-time linear time-invariant systems. The scheme uses a
purely data-driven system parametrization to predict future trajectories based
on behavioral systems theory. The control objective is tracking of a given
input-output setpoint. We prove that this setpoint is exponentially stable for
the closed loop of the proposed MPC, if it is reachable by the system dynamics
and constraints. For an unreachable setpoint, our scheme guarantees closed-loop
exponential stability of the optimal reachable equilibrium. Moreover, in case
the system dynamics are known, the presented results extend the existing
results for model-based setpoint tracking to the case where the stage cost is
only positive semidefinite in the state. The effectiveness of the proposed
approach is illustrated by means of a practical example.
