Conformal Koopman for Embedded Nonlinear Control with Statistical Robustness: Theory and Real-World Validation

TL;DR

This paper introduces a data-driven Koopman-based control framework that uses conformal prediction to provide formal safety guarantees and robustness for nonlinear systems, validated on simulations and real-world drone experiments.

Contribution

It establishes a novel connection between Koopman operators and contraction theory, integrating conformal prediction into a closed-loop control architecture for robustness.

Findings

Provides probabilistic bounds on state tracking error under uncertainty.

Demonstrates safety and robustness in drone control experiments.

Achieves accurate tracking with formal guarantees.

Abstract

We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers distribution-free probabilistic bounds on the state tracking error under Koopman modeling uncertainty. Conformal prediction is employed here to rigorously derive a bound on the state-dependent modeling uncertainty throughout the trajectory, ensuring safety and robustness without assuming a specific error prediction structure or distribution. Unlike prior approaches that merely combine conformal prediction with Koopman-based control in an open-loop setting, our method establishes a closed-loop control architecture with formal guarantees that explicitly account for both forward and inverse modeling errors. Also, by expressing the tracking error bound in terms of the control parameters and the modeling errors, our framework offers a quantitative means to formally enhance the performance of arbitrary Koopman-based control. We validate our method both in numerical simulations with the Dubins car and in real-world experiments with a highly nonlinear flapping-wing drone. The results demonstrate that our method indeed provides formal safety guarantees while maintaining accurate tracking performance under Koopman modeling uncertainty.