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. 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.

On the Certainty-Equivalence Approach to Direct Data-Driven LQR Design / Dorfler, Florian; Tesi, Pietro; De Persis, Claudio. - In: IEEE TRANSACTIONS ON AUTOMATIC CONTROL. - ISSN 0018-9286. - ELETTRONICO. - (2023), pp. 1-8. [10.1109/TAC.2023.3253787]

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

Tesi, Pietro;
2023

Abstract

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. 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.
2023
1
8
Dorfler, Florian; Tesi, Pietro; De Persis, Claudio
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1330734
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