Robust Conformal CBF and CLF Controllers via Iterative Policy Updates

2026-06-13

AI Summary

This work addresses the challenge that existing conformal prediction–based CLF/CBF controllers struggle to guarantee system stability and safety due to distribution shifts induced by closed-loop policy updates. To overcome this limitation, the paper proposes a phased iterative update strategy that integrates adversarially robust conformal prediction with a distribution shift budget during each policy optimization step. Notably, it provides the first theoretical guarantees of cross-iteration stability and safety for robust conformal CLF/CBF methods. Leveraging trajectory sensitivity analysis, the authors design both explicit and implicit update rules for conformal prediction boundaries. Empirical validation across three case studies demonstrates that the proposed approach achieves safe and stable control performance with rigorous theoretical assurances.

Abstract

Conformal prediction (CP) has been used to obtain probabilistic bounds on the error between a learned dynamics model and the true but unknown system. Such CP bounds can then be embedded into robust control Lyapunov function (CLF) and control barrier function (CBF) frameworks. However, such an approach does not retain stability/safety guarantees because of the distribution shift between the closed-loop trajectory distribution under the deployed CLF/CBF policy and the trajectory distribution from which the CP bound and its guarantees were derived. To address this issue, we propose an episodic framework that iteratively updates the robust conformal CLF/CBF policy while maintaining stability/safety guarantees across episodes. We achieve this by (1) using adversarially robust conformal prediction, and (2) quantifying a distribution shift budget that allows us to control how much the model error can increase across policy updates. This distribution shift budget is derived via a closed-loop trajectory sensitivity analysis, yielding an implicit and an explicit update rule for the CP bound. We analyze convergence of our algorithm, which we demonstrate on three case studies. To the best of our knowledge, these are the first results that provide stability/safety guarantees for robust conformal CBF/CLF policies.

Problem

• Conformal Prediction
• Control Barrier Function
• Control Lyapunov Function
• Distribution Shift
• Stability and Safety Guarantees

Innovation

• Conformal Prediction
• Control Barrier Function
• Control Lyapunov Function
• Distribution Shift
• Robust Control