  In this paper, we consider the design of data-driven predictive controllers
for nonlinear systems from input-output data via linear-in-control input
Koopman lifted models. Instead of identifying and simulating a Koopman model to
predict future outputs, we design a subspace predictive controller in the
Koopman space. This allows us to learn the observables minimizing the
multi-step output prediction error of the Koopman subspace predictor,
preventing the propagation of prediction errors. To avoid losing feasibility of
our predictive control scheme due to prediction errors, we compute a terminal
cost and terminal set in the Koopman space and we obtain recursive feasibility
guarantees through an interpolated initial state. As a third contribution, we
introduce a novel regularization cost yielding input-to-state stability
guarantees with respect to the prediction error for the resulting closed-loop
system. The performance of the developed Koopman data-driven predictive control
methodology is illustrated on a nonlinear benchmark example from the
literature.
