  This work proposes a robust data-driven predictive control approach for
unknown nonlinear systems in the presence of bounded process and measurement
noise. Data-driven reachable sets are employed for the controller design
instead of using an explicit nonlinear system model. Although the process and
measurement noise are bounded, the statistical properties of the noise are not
required to be known. By using the past noisy input-output data in the learning
phase, we propose a novel method to over-approximate reachable sets of an
unknown nonlinear system. Then, we propose a data-driven predictive control
approach to compute safe and robust control policies from noisy online data.
The constraints are guaranteed in the control phase with robust safety margins
through the effective use of the predicted output reachable set obtained in the
learning phase. Finally, a numerical example validates the efficacy of the
proposed approach and demonstrates comparable performance with a model-based
predictive control approach.
