  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.
