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

2021/09/05 by Henk J. van Waarde, van Waarde, Henk J., M. Kanat Camlibel +5 · 10 citations
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Scientific Research and Discoveries #math.OC

paper · pdf · doi:10.48550/arxiv.2109.02090

arxiv created 2021/09/05 · openalex publication_date 2021/09/05 · arxiv updated 2021/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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