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

2026-03-23

AI Summary

This work addresses the lack of statistical guarantees on tracking error and safety in data-driven nonlinear control arising from modeling uncertainties in Koopman operator-based approaches. To this end, the paper proposes a closed-loop control framework that integrates Koopman operators, contraction theory, and conformal prediction. Notably, it introduces distribution-free conformal prediction into Koopman-based control for the first time, explicitly characterizing both forward and inverse modeling errors. This integration yields quantifiable probabilistic bounds on tracking error, thereby enabling high-precision control with statistically robust safety assurances. The effectiveness of the proposed method is validated through simulations on a Dubins car and real-world experiments on a flapping-wing unmanned aerial vehicle, demonstrating its ability to simultaneously ensure safety and tracking performance under significant modeling uncertainty.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Data transparency and provenance
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Koopman operator
• statistical robustness
• conformal prediction
• nonlinear control
• modeling uncertainty

Innovation

• Conformal Prediction
• Koopman Operator
• Statistical Robustness
• Closed-loop Control
• Nonlinear Systems