Stability of Data-Driven Predictive Control for Nonlinear Systems via Koopman Embeddings

Data-driven model predictive control (MPC) based on Willems' fundamental lemma has proven effective for linear systems, but extending its stability guarantees to nonlinear systems remains an open challenge. In this letter, we establish conditions under which data-driven MPC, applied directly to input-output data from a nonlinear system, yields practical exponential stability. The key insight is that the existence of an approximate Koopman linear embedding lets the nonlinear data be interpreted as noisy data from a linear time-invariant system, bringing the problem within the scope of existing robust data-driven MPC theory. Crucially, the embedding serves only as a theoretical certificate: the controller operates on raw nonlinear data without using the lifting functions. We further show that the proportional structure of the Koopman residual yields an asymptotic bound determined by the offset c0 of the embedding error rather than by its worst-case magnitude over the operating region. The framework is demonstrated on a synchronous generator connected to an infinite bus, for which we construct an explicit physicsinformed embedding with error bounds.