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

Authors

Henk J. van Waarde, M. Kanat Camlibel, Mehran Mesbahi

Year

2020

Journal Paper

Algorithm

Matrix S-Lemma

Source

IEEE Transactions on Automatic Control

Identifiers

arXiv 2006.00870 DOI 10.1109/TAC.2020.3047577

Abstract¶

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 paper. We provide both strict and non-strict versions of this S-lemma, that are of interest in their own right. Thereafter, we will apply these results to data-driven control. In particular, we will derive non-conservative design methods for quadratic stabilization, H_2 and H_inf 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 data sets.

Summary¶

Uses a matrix S-lemma to derive exact, nonconservative LMI conditions for controller synthesis from noisy input-state data. The result is a central technical tool for the informativity framework because it converts sets of data-consistent systems into tractable robust-control inequalities.