The model is wrong. The controller works anyway, with proof.
Koopman operator theory lifts nonlinear dynamics into a linear space: instead of tracking the state directly, track a set of observables that evolve linearly. The linear model enables powerful control techniques — LQR, MPC, spectral analysis — on systems that are inherently nonlinear. The catch: the lifted model is always an approximation, and the approximation error can violate safety guarantees.
Conformal Koopman (arXiv:2603.21580): wrap the Koopman controller in conformal prediction. Distribution-free probabilistic bounds on the state tracking error under modeling uncertainty. No assumptions about the error distribution — the guarantee holds for any distribution, provided the calibration data is exchangeable with the test data.
The framework bounds both forward modeling errors (how well the Koopman model predicts the next state) and inverse modeling errors (how well the controller computed from the Koopman model actually controls the real system). The tracking error bounds are expressed through control parameters and modeling errors, enabling quantitative improvement — tighten the bound by either improving the model or adjusting the controller.
Validated on a flapping-wing drone — a system with complex, nonlinear aerodynamics that no first-principles model captures accurately. The Koopman model is necessarily approximate. The conformal bounds are necessarily valid. The combination produces a controller that works despite model error, with formal safety guarantees that don't depend on the model being right.
The structural principle: the guarantee comes from the statistics, not the model. The model provides performance (it steers the drone). The conformal prediction provides safety (it bounds how far the drone can deviate). Separating the two concerns — model for performance, statistics for safety — is more robust than demanding a model accurate enough to guarantee safety on its own.