Dissipativity verification with guarantees for polynomial systems from noisy input-state data

TL;DR

This paper develops a method to verify dissipativity in polynomial systems directly from noisy input-state data without explicit model identification, using sum of squares optimization for rigorous guarantees.

Contribution

It introduces two noise characterization methods and set-membership representations enabling noise-robust dissipativity verification from data.

Findings

Able to verify dissipativity over finite horizons from noisy data

Provides computationally tractable SOS-based verification conditions

Ensures rigorous guarantees despite measurement noise

Abstract

In this paper, we investigate the verification of dissipativity properties for polynomial systems without an explicitly identified model but directly from noise-corrupted measurements. Contrary to most data-driven approaches for nonlinear systems, we determine dissipativity properties over all finite time horizons using noisy input-state data. To this end, we propose two noise characterizations to deduce two data-based set-membership representations of the ground-truth system. Each representation then serves as a framework to derive computationally tractable conditions to verify dissipativity properties with rigorous guarantees from noise-corrupted data using sum of squares (SOS) optimization.