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

Amin Taghieh and SangWoo Park have published a significant theoretical advance in control theory, establishing conditions under which purely data-driven Model Predictive Control (MPC) can guarantee stability for complex, nonlinear systems. Their paper, "Stability Guarantees for Data-Driven Predictive Control of Nonlinear Systems via Approximate Koopman Embeddings," bridges a critical gap: while data-driven MPC based on Willems' fundamental lemma works well for linear systems, extending formal stability guarantees to nonlinear systems has remained an open challenge. The researchers prove that if a nonlinear system admits an approximate Koopman linear embedding—a mathematical representation that lifts nonlinear dynamics into a higher-dimensional linear space—then the raw data from that system can be interpreted as noisy measurements from a linear time-invariant system.

This conceptual breakthrough allows the application of existing robust stability theories for linear systems to the nonlinear case. Crucially, the Koopman embedding serves only as a theoretical certificate; the actual controller is implemented directly on the raw, nonlinear input-output data without needing to know or compute the complex lifting functions. The team further refined their analysis by showing that the structure of the embedding error can be exploited to derive an ultimate performance bound that depends only on an irreducible offset, not the worst-case error. They validated their framework with a practical demonstration, constructing an explicit physics-informed embedding with calculable error bounds for a synchronous generator connected to an infinite bus—a classic and critical problem in power system stability.