Koopman-based output-feedback control guarantees stability for nonlinear systems

A major challenge in nonlinear control is designing feedback laws that work with only input-output measurements, while still guaranteeing closed-loop stability. Existing data-driven methods with rigorous guarantees typically require full state measurements, limiting their real-world applicability. A team led by Robin Strässer, Julian Berberich, Manuel Schaller, Karl Worthmann, and Frank Allgöwer now addresses this gap by combining Koopman operator theory with an extended state representation built directly from input-output trajectories. This yields a bilinear surrogate model—a mathematically tractable structure—that enables the use of robust state-feedback design techniques. By exploiting observability of the underlying nonlinear system, the authors prove exponential stability of the extended state, which in turn ensures exponential convergence of the original system state to the origin. The approach is validated via numerical simulations, demonstrating that the method works without any knowledge of the full state.

The significance lies in bridging theoretical rigor with practical data-driven control. Traditional output-feedback methods often rely on separate state estimation (e.g., observers), adding complexity and potential instability. The proposed technique eliminates that step by directly learning a model from input-output data and providing guaranteed performance. This is particularly valuable for complex nonlinear systems where sensors are limited or expensive—such as robotics, chemical processes, or autonomous vehicles. The paper, published on arXiv (arXiv:2606.07758), also opens avenues for extending Koopman-based methods to more general settings, including systems with disturbances or uncertainties. For engineers and researchers, it offers a principled way to design controllers that are both data-efficient and safety-certifiable.