On the Certainty-Equivalence Approach to Direct Data-Driven LQR Design

• 成果类型: Article
• 署名作者: Dorfler, Florian; Tesi, Pietro; De Persis, Claudio
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Florence; University of Groningen
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3253787
• 发表日期: 2023
• 页码: 7989-7996
• 关键词: Data-driven modeling; linear feedback control systems; optimal control

摘要

The linear quadratic regulator (LQR) problem is a cornerstone of automatic control, and it has been widely studied in the data-driven setting. The various data-driven approaches can be classified as indirect (i.e., based on an identified model) versus direct or as robust (i.e., taking uncertainty into account) versus certainty-equivalence. Here, we show how to bridge these different formulations and propose a novel, direct, and regularized formulation. We start from indirect certainty-equivalence LQR, i.e., least-square identification of state-space matrices followed by a nominal model-based design, formalized as a bilevel program. We show how to transform this problem into a single-level, regularized, and direct data-driven control formulation, where the regularizer accounts for the least-square data fitting criterion. For this novel formulation, we carry out a robustness and performance analysis in presence of noisy data. In a numerical case study, we compare regularizers promoting either robustness or certainty-equivalence, and we demonstrate the remarkable performance when blending both of them.