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

arXiv: https://arxiv.org/abs/2008.03231 · HTML: https://mlsanity.com/paper/2008.03231/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2020.

## Built on by (most cited first, 2 of 2)

- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [Data-driven Set-based Estimation of Polynomial Systems with Application to SIR Epidemics](https://mlsanity.com/paper/2111.04704/) (2021)

## Abstract (arXiv)

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.