2021/09/14 by Florian Dörfler, Pietro Tesi, Dörfler, Florian +3 · 3 citations
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Mathematics #Fault Detection and Control Systems #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2109.06643
openalex publication_date 2021/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 bi-level 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. Our proposed direct and regularized formulation is also amenable to be further blended with a robust-stability-promoting regularizer. 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.