  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.
