  In this paper, we present a data-driven model predictive control (MPC) scheme
that is capable of stabilizing unknown linear time-invariant systems under the
influence of process disturbances. To this end, Willems' lemma is used to
predict the future behavior of the system. This allows the entire scheme to be
set up using only a priori measured data and knowledge of an upper bound on the
system order. First, we develop a state-feedback MPC scheme, based on
input-state data, which guarantees closed-loop practical exponential stability
and recursive feasibility as well as closed-loop constraint satisfaction. The
scheme is extended by a suitable constraint tightening, which can also be
constructed using only data. In order to control a priori unstable systems, the
presented scheme contains a pre-stabilizing controller and an associated input
constraint tightening. We first present the proposed data-driven MPC scheme for
the case of full state measurements, and also provide extensions for obtaining
similar closed-loop guarantees in case of output feedback. The presented scheme
is applied to a numerical example.
