Formally Guaranteed Control Adaptation for ODD-Resilient Autonomous Systems

Safety-critical control of uncertain, adaptive systems often relies on conservative, worst-case uncertainty bounds that limit closed-loop performance. Online conformal prediction is a powerful data-driven method for quantifying uncertainty when truth values of predicted outputs are revealed online; however, for systems that adapt the dynamics without measurements of the state derivatives, standard online conformal prediction is insufficient to quantify the model uncertainty. We propose Staggered Integral Online Conformal Prediction (SI-OCP), an algorithm utilizing an integral score function to quantify the lumped effect of disturbance and learning error. This approach provides long-run coverage guarantees, resulting in long-run safety when synthesized with safety-critical controllers, including robust tube model predictive control. Finally, we validate the proposed approach through a numerical simulation of an all-layer deep neural network (DNN) adaptive quadcopter using robust tube (MPC), highlighting the applicability of our method to complex learning parameterizations and control strategies.

In safety-critical Cyber-Physical Systems (CPS), trajectory prediction guides downstream planning and control. Deep learning models forecast well on validation data, but their reliability drops in out-of-distribution (OOD) scenarios driven by environmental uncertainty or rare traffic behaviors [1, 2]. Such failures are often silent: forecasts stay spatially plausible while accuracy collapses, and reported uncertainty does not rise [3]. Detection is hard because traffic conditions and interaction patterns keep evolving, yet the safety-critical nature of autonomous driving (AD) demands formal guarantees on detection delay and false-alarm rate. Following [4], we reframe OOD monitoring as quickest changepoint detection (QCD), a principled statistical framework with well-established theory. We find that the evolution of prediction errors on in-distribution (ID) data is well modeled by a Hidden Markov Model (HMM). Building on this, we extend a recent cumulative Maximum Mean Discrepancy approach to our setting. The method needs no detailed prior knowledge of the post-change distribution, yet admits provable delay and false-alarm guarantees. On three real-world driving datasets, it reduces detection delay while staying robust to heavy-tailed distributions and unknown post-change conditions.

Control barrier functions are an effective model-based tool to formally certify the safety of a system. However, transferring their theoretical guarantees to real-world robotics systems requires high model fidelity. For example, payloads or wind disturbances can cause significant model perturbations to an aerial vehicle, leading to safety compromises. In this work, we propose a certifiable online learning-enhanced robust adaptive control barrier function, which adapts to disturbances using a Neural ODE and quantifies its adaptation uncertainty with conformal prediction. Our approach guarantees safety at all time under unknown time-varying model disturbances. It adopts a conservative strategy when the adaptation uncertainty is high; and efficiently adapts to reduce controller conservativeness as it receives more data. Our approach provides a provable safety guarantee with a probability bound under suitable Lipschitz smoothness assumptions on the underlying model and trajectory. These results demonstrate the potential of our method as a practical safety controller for robotics system operating under model perturbations.