On Regularizability and its Application to Online Control of Unstable LTI Systems

• URL: http://arxiv.org/abs/2006.00125v3
• Date: Wed, 19 Jan 2022 21:04:25 GMT
• Title: On Regularizability and its Application to Online Control of Unstable LTI Systems
• Authors: Shahriar Talebi, Siavash Alemzadeh, Niyousha Rahimi and Mehran Mesbahi
• Abstract summary: We examine online regulation of (possibly unstable) partially unknown linear systems with no prior access to an initial stabilizing controller or PE input-output data. Having access only to the input matrix, we propose the Data-Guided Regulation (DGR) procedure that regulates the underlying state while also generating informative data. 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.
• Score: 0.5735035463793007
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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