Learn and Control while Switching: with Guaranteed Stability and Sublinear Regret

TL;DR

This paper introduces a novel learning and control algorithm for over-actuated systems that switch between actuators, ensuring stability and achieving sublinear regret in unknown system settings.

Contribution

It proposes an OFU-based algorithm with stability guarantees and an optimal warm-up duration for switching actuators in linear quadratic systems.

Findings

Guarantees system stability during switching.

Achieves sublinear regret of order √T.

Outperforms naive OFU approaches.

Abstract

Over-actuated systems often make it possible to achieve specific performances by switching between different subsets of actuators. However, when the system parameters are unknown, transferring authority to different subsets of actuators is challenging due to stability and performance efficiency concerns. This paper presents an efficient algorithm to tackle the so-called "learn and control while switching between different actuating modes" problem in the Linear Quadratic (LQ) setting. Our proposed strategy is constructed upon Optimism in the Face of Uncertainty (OFU) based algorithm equipped with a projection toolbox to keep the algorithm efficient, regret-wise. Along the way, we derive an optimum duration for the warm-up phase, thanks to the existence of a stabilizing neighborhood. The stability of the switched system is also guaranteed by designing a minimum average dwell time. The proposed strategy is proved to have a regret bound of $\mathcal{\bar{O}}\big(\sqrt{T}\big)+\mathcal{O}\big(ns\sqrt{T}\big)$ in horizon $T$ with $(ns)$ number of switches, provably outperforming naively applying the basic OFU algorithm.