# Statistical Guarantees in Data-Driven Nonlinear Control: Conformal Robustness for Stability and Safety

arXiv: https://arxiv.org/abs/2506.06228 · HTML: https://mlsanity.com/paper/2506.06228/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2025.

## Built on by (most cited first, 3 of 3)

- [When Environments Shift: Safe Planning with Generative Priors and Robust Conformal Prediction](https://mlsanity.com/paper/2602.12616/) (2026)
- [Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systems](https://mlsanity.com/paper/2603.07092/) (2026)
- [Statistical Convergence of Transformer Encoder-Accelerated Robust Reinforcement Learning](https://mlsanity.com/paper/2609.23775/) (2026)

## Abstract (arXiv)

We present a true-dynamics-agnostic, statistically rigorous framework for establishing exponential stability and safety guarantees of closed-loop, data-driven nonlinear control. Central to our approach is the novel concept of conformal robustness, which robustifies the Lyapunov and zeroing barrier certificates of data-driven dynamical systems against model prediction uncertainties using conformal prediction. It quantifies these uncertainties by leveraging rank statistics of prediction scores over system trajectories, without assuming any specific underlying structure of the prediction model or distribution of the uncertainties. With the quantified uncertainty information, we further construct the conformally robust control Lyapunov function (CR-CLF) and control barrier function (CR-CBF), data-driven counterparts of the CLF and CBF, for fully data-driven control with statistical guarantees of finite-horizon exponential stability and safety. The performance of the proposed concept is validated in numerical simulations with four benchmark nonlinear control problems.