⚡ electrical engineering

CC-DeePC: Adaptive Conformal Calibration for Safe Data-Enabled Predictive Control under Non-Stationary Dynamics

This paper proposes CC-DeePC, a safe data-enabled predictive control framework that leverages Adaptive Conformal Inference to dynamically calibrate output constraints based on predictor residuals, thereby significantly increasing the rate of certified, slack-free safety under non-stationary dynamics compared to existing robust and static baselines.

Original authors: Md Hasibuzzaman, Chan-Yun Yang, Gene Eu Jan

Published 2026-08-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Md Hasibuzzaman, Chan-Yun Yang, Gene Eu Jan

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a robot moving through a world that is constantly changing. The ground beneath its wheels might become slippery, its cargo might shift, or the wind might suddenly pick up. To move safely, the robot must predict what will happen next and decide how to steer. If its prediction is wrong, it could crash or veer off a safe path. For decades, engineers have tried to build robots that learn from their own past movements to make these predictions, a method that works well when the world stays the same. But when the environment shifts unexpectedly, these old methods often fail because they rely on a fixed set of rules that no longer match reality. The challenge is to keep the robot safe without making it so cautious that it stops moving entirely.

Researchers have developed a new approach called CC-DeePC to solve this problem. Instead of guessing how the world might change, this system watches its own mistakes in real time. Every time the robot predicts where it will be one second from now and then checks where it actually is, it measures the difference. If the difference is small, the robot knows its prediction is good. If the difference is large, it knows something has changed. The new method uses a mathematical tool called adaptive conformal inference to turn these past mistakes into a safety buffer. It constantly adjusts how much extra space the robot needs to stay safe. If the robot starts making bigger mistakes, the system automatically widens the safety zone. If the robot is doing well, it tightens the zone to allow for smoother, more efficient movement. This happens without needing to know exactly why the world changed or to assume the changes follow a predictable pattern.

The researchers tested this system on a simulated robot designed to track a specific speed. They created scenarios where the robot's behavior changed suddenly, like a car hitting a patch of ice, or gradually, like a vehicle slowly picking up a heavy load. They compared their new method against several older strategies. One older strategy used a fixed, very large safety margin, ensuring the robot never crashed but often moving very slowly and awkwardly. Another used a fixed margin based on past data, which worked well until the world changed, at which point it failed silently. The new adaptive method performed just as well as the best fixed strategies in terms of how often the robot actually broke the safety rules. However, the way it achieved this safety was fundamentally different and more reliable.

The key discovery was that the new method kept the robot safe because its predictions were actually correct, not because it was relying on a numerical "escape hatch." The older methods often appeared safe only because they allowed the robot to break its own safety rules slightly, using a hidden penalty to absorb the error. The new method, by contrast, ensured that the robot stayed within its safe limits because the safety buffer it calculated was genuinely accurate. In tests involving one hundred different scenarios, the new method achieved a "clean safety" rate that was three to seven times higher than the best fixed methods. This means that for the vast majority of the time, the robot was safe because its math was right, not because it was relying on a hidden penalty.

The researchers also tested the system on a more complex robot with two wheels and on a simulated vehicle using real-world driving data from a highway. In every case, the adaptive method maintained this high level of certified safety. However, they found a limit to its power. When they moved the test to a two-dimensional navigation task where the robot had to dodge moving obstacles using a sensor that sometimes gave imperfect readings, the advantage disappeared. In this difficult setting, the system could not distinguish itself from the older methods, and the robot had to take much longer, winding paths to avoid collisions. This suggests that while the method is excellent for controlling a vehicle's speed and direction, it struggles when the environment is chaotic and the sensors are noisy.

Ultimately, this work provides a way for machines to stay safe in a shifting world without needing to be overly conservative. It proves that a robot can learn to adjust its own safety margins on the fly, reacting to its own errors to stay within safe bounds. The system does not require a perfect model of the world or a guarantee that conditions will remain stable. It simply watches, learns from its mistakes, and adjusts its safety zone accordingly. While it is not a magic solution for every possible situation, particularly when sensors are unreliable, it offers a robust and mathematically sound way to keep autonomous systems safe when the ground beneath them begins to change.

Technical Summary: CC-DeePC

Problem Statement
Data-Enabled Predictive Control (DeePC) regulates unknown systems directly from measured input-output trajectories using a behavioral predictor (Hankel matrix representation). However, the reliability of this predictor is contingent on the data window used for its construction. When system dynamics are non-stationary (e.g., drifting friction coefficients or changing payloads), the predictor's validity degrades. Existing robustness approaches, such as fixed regularization or static distributionally-robust ambiguity sets, are calibrated offline and do not adapt to these shifts, leading to silent failures where safety guarantees degrade as dynamics drift away from the calibration data. Furthermore, prior work on conformal prediction for safety has largely focused on calibrating uncertainty around external agents (e.g., other vehicles) rather than the ego system's own data-driven predictor.

Methodology: CC-DeePC
The authors propose CC-DeePC (Conformally-Calibrated DeePC), a variant that integrates Adaptive Conformal Inference (ACI) directly into the DeePC receding-horizon control loop.

Core Mechanism: Instead of relying on external agents or static margins, CC-DeePC calibrates the output constraint margin ( $m_t$ ) using the controller's own realized one-step prediction residuals ( $s_t = |y_{t+1} - \hat{y}_{t+1|t}|$ ).
Online Recalibration: The method employs an ACI recursion to update a miscoverage level $\alpha_t$ based on whether the current residual exceeds the current margin. The margin $m_{t+1}$ is then set to the empirical quantile of a sliding buffer of recent residuals corresponding to the updated $\alpha_{t+1}$ .
Soft-Constrained Optimization: The control problem is formulated as a soft-constrained Quadratic Program (QP). The output constraints are tightened by the margin $m_t$ (i.e., $y + m_t \leq \hat{y} \leq \bar{y} - m_t$ ). To ensure feasibility under transient conditions where the tightened box might be unreachable, heavily penalized slack variables ( $s_{lo}, s_{hi}$ ) are introduced.
Theoretical Guarantees:
- Proposition 1: Proves a finite-horizon empirical miscoverage bound on the residual sequence under arbitrary non-stationary dynamics, without requiring exchangeability or stationarity assumptions.
- Lemma 1 & Corollary 1: Establish a sufficient condition connecting residual coverage to physical constraint safety. Specifically, if the slack variables are inactive (zero) and the residual is covered by the margin, the physical output is guaranteed to satisfy the safety bounds. This bridges the gap between the theoretical residual bound and actual physical safety.

Key Contributions

Formulation: The integration of online ACI updates into a soft-constrained DeePC framework, creating a controller that recalibrates its own safety margins based on realized performance.
Theoretical Bridge: Providing a rigorous proof (Proposition 1) for residual coverage under non-stationarity and an explicit sufficient condition (Lemma 1) linking this coverage to physical safety, distinguishing between "certified safety" (satisfied via the margin) and "fallback safety" (satisfied via slack variables).
Empirical Validation: A comprehensive benchmark against four baselines (Nominal, Fixed Worst-Case, Static Conformal, and Fixed Distributionally-Robust) across Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) systems, including real-data extensions and 2D obstacle avoidance.

Results

Performance vs. Robustness: Under abrupt and gradual drift, CC-DeePC's raw violation rates and tracking RMSE are statistically indistinguishable from the Fixed Distributionally-Robust (DR-DeePC) baseline. However, unlike DR-DeePC, CC-DeePC does not rely on extreme conservatism to achieve these metrics.
Clean-Safety Rate: The most significant finding is the "clean-safety rate" (the fraction of steps where safety is achieved without activating the soft slack). CC-DeePC achieves a clean-safety rate 3.6–7× higher than DR-DeePC and 1.4–1.9× higher than Static Conformal methods. This indicates that CC-DeePC's safety performance is grounded in the validity of its calibrated interval rather than the QP's numerical fallback.
Causal Isolation: Ablation studies confirm that the performance gain is driven specifically by the ACI recursion (the online update of $\alpha_t$ ), not merely by using a sliding window of fresh data.
Extensions:
- Real Data: When applied to drift parameters fitted from real NGSIM vehicle trajectory data, CC-DeePC maintained a significantly higher clean-safety rate while requiring a 3–10× smaller margin than fixed baselines.
- 2D Navigation: In a harder 2D obstacle-avoidance task with LiDAR sensing (imperfect state estimation), CC-DeePC reduced collision rates compared to nominal and static baselines but incurred higher tracking errors and path lengths. Crucially, the "clean-safety" advantage diminished in this setting, becoming statistically indistinguishable from other baselines, highlighting the method's sensitivity to sensing imperfections.

Significance and Claims
The paper claims that CC-DeePC offers a distinct advantage not in raw violation rates (where it is often tied with robust baselines) but in the certifiability of that safety. The authors argue that standard robust methods often achieve low violation rates by relying on "uncertified fallbacks" (heavy slack activation), whereas CC-DeePC grounds its performance in a distribution-free, online-calibrated guarantee.

The authors are modest about their claims, acknowledging:

The method does not universally outperform fixed baselines on raw metrics (RMSE or violation rate).
The "clean-safety" advantage is not universal; it can degrade to statistical insignificance under realistic sensing imperfections and moving obstacles.
The method exhibits a transient over-conservatism (large margins) immediately following abrupt dynamic shifts, a known trade-off of the ACI mechanism.
The current MIMO extension uses a scalarized nonconformity score rather than a fully multivariate calibration.

The work positions CC-DeePC as a step toward safe, data-driven control under non-stationary dynamics, emphasizing the importance of distinguishing between safety achieved through valid prediction intervals versus safety achieved through numerical relaxation.

Technical Summary: CC-DeePC

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