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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| Published in | IEEE transactions on automatic control Vol. 67; no. 1; pp. 162 - 175 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.01.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 1558-2523 |
| DOI | 10.1109/TAC.2020.3047577 |
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| Abstract | 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. |
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| AbstractList | 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. 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, [Formula Omitted] and [Formula Omitted] 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. |
| Author | Camlibel, M. Kanat van Waarde, Henk J. Mesbahi, Mehran |
| Author_xml | – sequence: 1 givenname: Henk J. orcidid: 0000-0002-2561-2682 surname: van Waarde fullname: van Waarde, Henk J. email: h.j.van.waarde@rug.nl organization: Bernoulli Institute for Mathematics, Computer Science, and Artificial Intelligence and the Engineering and Technology Institute Groningen, University of Groningen, Groningen, The Netherlands – sequence: 2 givenname: M. Kanat orcidid: 0000-0002-2407-8166 surname: Camlibel fullname: Camlibel, M. Kanat email: m.k.camlibel@rug.nl organization: Bernoulli Institute for Mathematics, Computer Science, and Artificial Intelligence, University of Groningen, Groningen, The Netherlands – sequence: 3 givenname: Mehran orcidid: 0000-0001-6972-6588 surname: Mesbahi fullname: Mesbahi, Mehran email: mesbahi@aa.washington.edu organization: William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, WA, USA |
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| SubjectTerms | 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 |
| Title | From Noisy Data to Feedback Controllers: Nonconservative Design via a Matrix S-Lemma |
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