From Noisy Data to Feedback Controllers: Nonconservative Design via a Matrix S-Lemma

In this article, we propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient of our design is a new matrix S-lemma that will be proven in this article. We provide both strict and nonstrict versions of this S-lemma, wh...

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Veröffentlicht in:IEEE transactions on automatic control Jg. 67; H. 1; S. 162 - 175
Hauptverfasser: van Waarde, Henk J., Camlibel, M. Kanat, Mesbahi, Mehran
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.01.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Control design
Control systems
Covariance matrices
Data-driven control
Feedback control
Independent variables
Linear matrix inequalities
LMIs
Mathematical analysis
Noise measurement
Optimal control
Predictive control
robust control
Tuning
uncertain systems
ISSN:0018-9286, 1558-2523
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Zusammenfassung:In this article, we propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient of our design is a new matrix S-lemma that will be proven in this article. We provide both strict and nonstrict versions of this S-lemma, which are of interest in their own right. Thereafter, we will apply these results to data-driven control. In particular, we will derive nonconservative design methods for quadratic stabilization, <inline-formula><tex-math notation="LaTeX">\mathcal {H}_2</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula> control, all in terms of data-based linear matrix inequalities. In contrast to previous work, the dimensions of our decision variables are independent of the time horizon of the experiment. Our approach, thus, enables control design from large datasets.
Bibliographie:ObjectType-Article-1
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2020.3047577