Data-driven dissipativity analysis: application of the matrix S-lemma

TL;DR

This paper introduces a data-driven method to verify dissipativity in linear systems directly from noisy measurements, bypassing the need for explicit system models, using linear matrix inequalities.

Contribution

It provides novel conditions for assessing dissipativity from finite noisy data samples under various noise models, formulated as solvable linear matrix inequalities.

Findings

Conditions for dissipativity verification from noisy data

Applicability to noise-free and bounded noise scenarios

Use of linear matrix inequalities for practical computation

Abstract

The concept of dissipativity, as introduced by Jan Willems, is one of the cornerstones of systems and control theory. Typically, dissipativity properties are verified by resorting to a mathematical model of the system under consideration. In this paper, we aim at assessing dissipativity by computing storage functions for linear systems directly from measured data. As our main contributions, we provide conditions under which dissipativity can be ascertained from a finite collection of noisy data samples. Three different noise models will be considered that can capture a variety of situations, including the cases that the data samples are noise-free, the energy of the noise is bounded, or the individual noise samples are bounded. All of our conditions are phrased in terms of data-based linear matrix inequalities, which can be readily solved using existing software packages.