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

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