Ensuring the Safety of Uncertified Linear State-Feedback Controllers via Switching

TL;DR

This paper introduces a switching strategy that enhances the safety of uncertified linear controllers by reverting to a known stabilizer when system states become large, ensuring bounded cost and near-optimal performance.

Contribution

It proposes a novel switching approach that guarantees safety and near-optimality for uncertain linear controllers, addressing destabilization issues caused by noise.

Findings

Switching strategy bounds the linear-quadratic cost under destabilizing controllers.

The performance loss due to switching is asymptotically negligible.

Simulation demonstrates effectiveness on an industrial process.

Abstract

Sustained research efforts have been devoted to learning optimal controllers for linear stochastic dynamical systems with unknown parameters, but due to the corruption of noise, learned controllers are usually uncertified in the sense that they may destabilize the system. To address this potential instability, we propose a "plug-and-play" modification to the uncertified controller which falls back to a known stabilizing controller when the norm of the state exceeds a certain threshold. We show that the switching strategy enhances the safety of the uncertified controller by making the linear-quadratic cost bounded even if the underlying linear feedback gain is destabilizing. We also prove the near-optimality of the proposed strategy by quantifying the maximum performance loss caused by switching as asymptotically negligible. Finally, we demonstrate the effectiveness of the proposed switching strategy using simulation on an industrial process example.