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Determining dissipativity for nonlinear systems from noisy data using Taylor polynomial approximation

In the literature of data-driven dissipativity verification, many approaches are restricted to linear systems or require knowledge on the basis functions of the nonlinear system dynamics. To overcome these limitations, this work proposes based on Taylor approximation a novel polynomial representation of nonlinear systems which can be learned from noise-corrupted measurements. Due to the polynomial characterization and the inclusion of the approximation error into the analysis, we can determine dissipativity properties for nonlinear dynamical systems from noisy data with rigorous guarantees, without explicitly identifying a model, and using computationally tractable sum of squares optimization.