Joint Stabilization and Regret Minimization through Switching in Over-Actuated Systems (extended version)

TL;DR

This paper introduces an optimism-based switching control algorithm for over-actuated systems that stabilizes the system and minimizes regret, achieving an $ ilde{O}( oot{T})$ regret bound.

Contribution

It presents a novel switching strategy combined with optimism in control for stabilizing over-actuated systems with proven regret bounds.

Findings

Achieves $ ilde{O}( oot{T})$ regret bound.

Effectively stabilizes systems during initial control phases.

Demonstrates the benefits of switching modes in control algorithms.

Abstract

Adaptively controlling and minimizing regret in unknown dynamical systems while controlling the growth of the system state is crucial in real-world applications. In this work, we study the problem of stabilization and regret minimization of linear over-actuated dynamical systems. We propose an optimism-based algorithm that leverages possibility of switching between actuating modes in order to alleviate state explosion during initial time steps. We theoretically study the rate at which our algorithm learns a stabilizing controller and prove that it achieves a regret upper bound of $\mathcal{O}(\sqrt{T})$.