Conformal Robust Control of Linear Systems

TL;DR

This paper introduces a data-driven, conformal prediction-based approach for robust control of linear systems, providing theoretical guarantees and improved empirical performance over traditional methods like $H_{ ext{infinity}}$ and multiplicative noise.

Contribution

It proposes a novel conformal prediction methodology for specifying uncertainty regions in LQR systems, with convergence-guaranteed policy gradient algorithms and superior empirical results.

Findings

Distribution-free coverage guarantees for uncertainty regions.

Efficient policy gradient method with convergence guarantees.

Outperforms traditional robust control methods in empirical tests.

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.