Data-driven system analysis of nonlinear systems using polynomial approximation

Tim Martin, Frank Allgöwer

Published 2021-08-25Version 1

In the context of data-driven system analysis of general nonlinear systems, there exist only few approaches which often lack on rigorous guarantees, call for nonconvex optimization, or require the knowledge of the basis functions of the system dynamics. In this paper, we establish a novel data-based non-parametric representation of nonlinear functions based on Taylor series which are derived from finite many noisy samples. By incorporating the measurement noise and the error of polynomial approximation, we provide computationally tractable conditions for sum of squares optimization, e.g., to verify dissipativity properties with rigorous guarantees and without an explicitly identified model.