  We present a robust data-driven control scheme for an unknown linear system
model with bounded process and measurement noise. Instead of depending on a
system model 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.
