Conformal Robust Control of Linear Systems

2024-05-25

arXiv.org

AI Summary

Addressing the dual challenges of theoretical guarantee gaps and empirical conservativeness in robust control of linear systems under model mismatch, this paper introduces conformal prediction into the LQR framework for the first time. It proposes a data-driven, distribution-free uncertainty modeling approach that provides statistically valid coverage guarantees for true system dynamics. Theoretically, it establishes a probabilistic characterization of regret—breaking away from deterministic robustness bounds in classical robust control. Algorithmically, it designs a novel policy gradient optimizer with provable convergence guarantees. Experiments on multiple engineering control systems demonstrate that the method achieves a superior trade-off between closed-loop performance and conservatism, significantly outperforming both H∞ control and multiplicative-noise LQR.

Technology Category

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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.

Problem

• Ensuring robust control under system dynamics misspecification
• Data-driven uncertainty specification using conformal prediction
• Efficient robust controller production with convergence guarantees

Innovation

• Uses conformal prediction for uncertainty regions
• Data-driven robust control with guarantees
• Novel policy gradient method with convergence