[论文解读] Conformal Koopman for Embedded Nonlinear Control with Statistical Robustness: Theory and Real-World Validation

Koki Hirano, Hiroyasu Tsukamoto|arXiv (Cornell University)|Mar 23, 2026

Model Reduction and Neural Networks被引用 0

一句话总结

该论文提出一种数据驱动、基于Koopman的控制框架，结合 conformal prediction 在潜在空间建模不确定性下提供无分布假设、有限样本的闭环跟踪保障，已在仿真和一台非线性拍翼无人机上验证。

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.

研究动机与目标

• Motivate the use of Koopman embeddings to linearize nonlinear dynamics for control with tractable analysis.
• Integrate conformal prediction to obtain distribution-free, finite-sample bounds on closed-loop tracking error under latent-space uncertainty.
• Establish a Lyapunov/ contraction-based framework that links latent-space stability to stability in the original nonlinear system.
• Provide explicit design guidelines that relate tracking performance bounds to controller gains and modeling errors.
• Validate the approach through numerical simulations and hardware experiments on a nonlinear aerial platform.

提出的方法

• Lift the nonlinear system into a finite-dimensional latent space with an encoder g and a decoder h, yielding a lifted linear model z_{k+1}=Az_{k}+Bu_{k}+d(x_{k},u_{k}).
• Describe two controllers: a Nominal Feedback Controller (NFC) and a Controller with Robust Disturbance Rejection (CRDR) that solves a convex optimization at each step to enforce contraction.
• Use contraction theory to show that latent-space stability implies original-system stability, via a contraction metric W(x)=G(x)^TMG(x).
• Define forward nonconformity scores for NFC and CRDR to quantify latent-space residuals and apply split conformal prediction to obtain probabilistic bounds on tracking error.
• Derive high-probability bounds on latent-space tracking error (Theorem 2) and state-space error (Theorem 3) that depend on controller parameters, decoder Lipschitz constant, and conformal quantiles.
• Demonstrate applicability with numerical tests on a Dubins car model and hardware experiments on a Flapper Nimble+ drone.

实验结果

研究问题

• RQ1 Can conformal prediction provide distribution-free guarantees on closed-loop tracking error for Koopman-based controllers with imperfect latent liftings?
• RQ2 How does linking latent-space contraction to original-system contraction enable formal safety guarantees in nonlinear control?
• RQ3 What is the quantitative relationship between controller gains, model uncertainty, and achievable tracking accuracy under the proposed framework?
• RQ4 Do the proposed NFC and CRDR controllers satisfy probabilistic safety and performance bounds in both simulation and real-world nonlinear platforms?

主要发现

• The framework yields high-probability bounds on latent-space tracking error under latent-space modeling uncertainty using conformal prediction.
• A quantitative link is established between closed-loop performance and controller design parameters, enabling principled learning-based Koopman control.
• CRDR outperforms NFC in tracking despite actuator limits, by enforcing contraction and robustly mitigating disturbances.
• The approach provides formal safety guarantees while maintaining accurate tracking in highly nonlinear systems, validated in both simulation (Dubins car) and hardware experiments (Flapper Nimble+ drone).
• Hardware validation confirms isotropic latent-space convergence (ratio of singular values near 1) and practical attainment of trajectory tracking bounds.