Conformal Koopman for Embedded Nonlinear Control with Statistical Robustness: Theory and Real-World Validation
This work addresses safety and robustness in embedded nonlinear control for applications like drones, though it is incremental as it builds on prior Koopman and conformal prediction methods.
The authors tackled the problem of controlling nonlinear systems with statistical robustness by proposing a data-driven Koopman-based framework that uses conformal prediction to derive probabilistic bounds on state tracking errors, validated through simulations and real-world experiments with a flapping-wing drone.
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.