Conformal Robust Control of Linear Systems
Yash Patel, Sahana Rayan, Ambuj Tewari
TL;DR
The paper addresses robust LQR design under dynamics misspecification by introducing a distribution-free conformal prediction framework to define uncertainty regions with provable coverage. It develops Conformalized Predict-Then-Control (CPC), a policy-gradient-based method that optimizes a robust objective over conformal uncertainty sets and provides convergence guarantees via gradient dominance. Empirical results across diverse engineering systems show CPC achieves lower robust regret and better stability than $\mathcal{H}_{\infty}$ and data-free margin methods, while calibration analyses validate the predicted coverage even with noisy dynamics. The approach enables principled, data-driven robustness in control co-design, with potential extensions to nonlinear settings and end-to-end CCD pipelines, offering practical impact for safe, reliable engineered systems.
Abstract
End-to-end engineering design pipelines, in which designs are evaluated using concurrently defined optimal controllers, are becoming increasingly common in practice. To discover designs that perform well even under the misspecification of system dynamics, such end-to-end pipelines have now begun evaluating designs with a robust control objective in place of the nominal optimal control setup. Current approaches of specifying such robust control subproblems, however, rely on hand specification of perturbations anticipated to be present upon deployment or margin methods that ignore problem structure, resulting in a lack of theoretical guarantees and overly conservative empirical performance. We, instead, propose a novel methodology for LQR systems that leverages conformal prediction to specify such uncertainty regions in a data-driven fashion. Such regions have distribution-free coverage guarantees on the true system dynamics, in turn allowing for a probabilistic characterization of the regret of the resulting robust controller. We then demonstrate that such a controller can be efficiently produced via a novel policy gradient method that has convergence guarantees. We finally demonstrate the superior empirical performance of our method over alternate robust control specifications, such as $H_{\infty}$ and LQR with multiplicative noise, across a collection of engineering control systems.