  We present a data-driven nonlinear predictive control approach for the class
of discrete-time multi-input multi-output feedback linearizable nonlinear
systems. The scheme uses a non-parametric predictive model based only on input
and noisy output data along with a set of basis functions that approximate the
unknown nonlinearities. Despite the noisy output data as well as the mismatch
caused by the use of basis functions, we show that the proposed multistep
robust data-driven nonlinear predictive control scheme is recursively feasible
and renders the closed-loop system practically exponentially stable. We
illustrate our results on a model of a fully-actuated double inverted pendulum.
