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.