Closed-loop guarantees from input–output data

Establish rigorous closed-loop guarantees—such as stability, feasibility, and performance—for Koopman-based control schemes when only input–output data are available rather than full state measurements. Specifically, determine conditions, identification procedures, and controller synthesis methods that ensure these guarantees under realistic observability and identifiability assumptions using input–output trajectories.

Background

The survey highlights that existing Koopman-based controller designs with guarantees typically assume access to input–state trajectories, i.e., full state measurements. In many real-world scenarios, only input–output data are available, which complicates identification, observability, and controller design.

Bridging this gap requires methods to build operator-theoretic models and robust controllers directly from input–output data while preserving closed-loop guarantees for the original nonlinear system. This challenge is central to broadening the practical applicability of Koopman-based control.

References

In many practical applications, however, only input–output data can be measured. Extending guarantees in Koopman-based control methods to handle this more realistic and restrictive setting remains an open problem.

— An overview of Koopman-based control: From error bounds to closed-loop guarantees  (2509.02839 - Strässer et al., 2 Sep 2025) in Section 6 (Conclusions and future research challenges), Summary box “Future research challenges”, Item 1

The second limitation is that the incorporation of feedback into the proposed feedforward design remains an open issue.

— Data-driven design of steady-state feedforward inputs for nonlinear systems under partial measurement  (2609.09450 - Raju et al., 8 Sep 2026) in Section 5, Conclusion and Future Works