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

• 成果类型: Article
• 署名作者: Talebi, Shahriar; Alemzadeh, Siavash; Rahimi, Niyousha; Mesbahi, Mehran
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3131148
• 发表日期: 2022
• 页码: 6413-6428
• 关键词: safety; Iterative control; online regulation; single trajectory learning; unstable linear systems

摘要

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 article, 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.