Provably robust verification of dissipativity properties from data

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.