Data-driven explicit reference governors for nonlinear systems via robust Koopman stabilization

Explicit reference governors (ERGs) enforce constraints with low online computational cost through Lyapunov-based safety margins. Their application to unknown nonlinear systems remains challenging, as the stabilizing controller and Lyapunov certificate required for admissible reference updates are generally unavailable. Koopman-based lifting provides a data-driven route to represent nonlinear dynamics in a higher-dimensional space where linear controller and Lyapunov-function synthesis becomes tractable. However, finite-dimensional approximation errors and disturbances may invalidate the safety margins used for admissible reference updates. This work proposes a Koopman-based robust data-driven ERG framework for unknown nonlinear systems. From open-loop input-state data, an uncertain lifted representation is constructed by decomposing the finite-dimensional Koopman residual into an input-dependent Lipschitz-bounded term and a bounded additive perturbation. A robust semidefinite program is then developed to synthesize a stabilizing feedback controller and an ERG-compatible quadratic Lyapunov certificate. The resulting Lyapunov function induces robust dynamic safety margins that explicitly account for lifted-model uncertainty. Embedding these margins into a discrete-time fast reference governor yields an explicit reference update law without online optimization. Theoretical analysis establishes closed-loop stability and recursive constraint satisfaction, and simulations demonstrate the effectiveness of the proposed approach.