Conformal Koopman for Embedded Nonlinear Control with Statistical Robustness: Theory and Real-World Validation
Koki Hirano and Hiroyasu Tsukamoto
AI summary
Problem
Existing Koopman-based control frameworks lack rigorous, distribution-free guarantees for closed-loop tracking error under modeling uncertainty, often relying on restrictive structural assumptions that may not hold in practice.
Approach
The authors connect Koopman operator theory with contraction theory and apply split conformal prediction to derive state-dependent probabilistic bounds on modeling uncertainty, enabling robust closed-loop controller design.
Key results
- Distribution-free probabilistic bounds on closed-loop tracking error via conformal prediction
- Formal equivalence between latent-space contraction and original system stability
- Quantitative design guidelines linking tracking precision to control gains and decoder Lipschitz constants
- Hardware validation on a highly nonlinear flapping-wing drone with accurate tracking under uncertainty
Why it matters
Provides safety-critical, statistically rigorous guarantees for learning-based nonlinear control without restrictive error assumptions, advancing reliable deployment of data-driven controllers in robotics.
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 guar- antees 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.