Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees

In this paper, we consider the design of data-driven predictive controllers for nonlinear systems from input-output data using 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, preventing the propagation of 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 closedloop system. The performance is illustrated on a nonlinear benchmark example from the literature.