Statistical Guarantees in Data-Driven Nonlinear Control: Conformal Robustness for Stability and Safety
For control engineers and researchers, this work offers a statistically rigorous method to certify stability and safety in data-driven control, addressing a key bottleneck in safe learning-based control.
The paper introduces conformal robustness, a framework that uses conformal prediction to provide statistical guarantees for exponential stability and safety in data-driven nonlinear control, without requiring knowledge of the true dynamics or uncertainty distributions. Simulations on four benchmarks validate the approach.
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.