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

By Henk van Waarde, M. Kanat Camlibel, Mehran Mesbahi. IEEE Transactions on Automatic Control, 2020

412 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c96fe84dc216474e80f4337f34fe0ac19c8314d0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Behavioral systems theory in data-driven analysis, signal processing, and control (2021, methodology): “…set of the measurement equation (56), { (B,A)| 0 = [B A ] [ U X ]} , the authors are able to cast this problem as a semidefinitess condition (van Waarde et al., 2020, Theorem 17): namely, the data (U,X) are informative for stabilization by state feedback if and only if there is a matrix Q…”
Data-Driven Dissipativity Analysis: Application of the Matrix S-Lemma (2021, methodology): “…H ∈ R p × p , and deﬁne With this notation in place, the problem of characterizing informativity for dissipativity is equivalent to ﬁnding conditions under which the inequality holds for all ( A, B, C, D ) satisfying Our strategy to solve this problem is to invoke the so called matrix S-lemma [26].”