  We present a robust data-driven control scheme for unknown linear systems
with a bounded process and measurement noise. Instead of depending on a system
model as in traditional predictive control, a controller utilizing data-driven
reachable regions is proposed. The data-driven reachable regions are based on a
matrix zonotope recursion and are computed based on only noisy input-output
data of a trajectory of the system. We assume that measurement and process
noise are contained in bounded sets. While we assume knowledge of these bounds,
no knowledge about the statistical properties of the noise is assumed. In the
noise-free case, we prove that the presented purely data-driven control scheme
results in an equivalent closed-loop behavior to a nominal model predictive
control scheme. In the case of measurement and process noise, our proposed
scheme guarantees robust constraint satisfaction, which is essential in
safety-critical applications. Numerical experiments show the effectiveness of
the proposed data-driven controller in comparison to model-based control
schemes.
