On Regularizability and its Application to Online Control of Unstable LTI Systems
Abstract
Learning, say through direct policy updates, often requires assumptions such as knowing a priori that the initial policy (gain) is stabilizing, or persistently exciting (PE) input-output data, is available. In this paper, we examine online regulation of (possibly unstable) partially unknown linear systems with no prior access to an initial stabilizing controller nor PE input-output data; we instead leverage the knowledge of the input matrix for online regulation. First, we introduce and characterize the notion of "regularizability" for linear systems that gauges the extent by which a system can be regulated in finite-time in contrast to its asymptotic behavior (commonly characterized by stabilizability/controllability). Next, having access only to the input matrix, we propose the Data-Guided Regulation (DGR) synthesis procedure that -- as its name suggests -- regulates the underlying state while also generating informative data that can subsequently be used for data-driven stabilization or system identification. We further improve the computational performance of DGR via a rank-one update and demonstrate its utility in online regulation of the X-29 aircraft.
Keywords
Cite
@article{arxiv.2006.00125,
title = {On Regularizability and its Application to Online Control of Unstable LTI Systems},
author = {Shahriar Talebi and Siavash Alemzadeh and Niyousha Rahimi and Mehran Mesbahi},
journal= {arXiv preprint arXiv:2006.00125},
year = {2022}
}