Provably robust verification of dissipativity properties from data

TL;DR

This paper introduces a data-driven framework for verifying dissipativity properties of systems directly from measurements, offering robustness guarantees even with noisy data, and demonstrates its effectiveness through real-world experiments.

Contribution

The paper develops a novel, non-conservative method for verifying dissipativity from data with robustness guarantees, extending to noisy input-output measurements and real-world applications.

Findings

Provides non-conservative conditions for noisy input-state data

Extends verification methods to noisy input-output data

Demonstrates applicability through real-world experiments

Abstract

Dissipativity properties have proven to be very valuable for systems analysis and controller design. With the rising amount of available data, there has therefore been an increasing interest in determining dissipativity properties from (measured) trajectories directly, while an explicit model of the system remains undisclosed. Most existing approaches for data-driven dissipativity, however, guarantee the dissipativity condition only over a finite time horizon and provide weak or no guarantees on robustness in the presence of noise. In this paper, we present a framework for verifying dissipativity properties from measured data with desirable guarantees. We first consider the case of input-state measurements, where we provide non-conservative and computationally attractive conditions in the presence of noise. We extend this approach to input-output data, where similar results hold in the noise-free case. We then provide results for the noisy input-output data case, which is particularly challenging. Finally, we apply the proposed approach in a real-world experiment and illustrate its applicability and advantages compared to established methods based on system identification.