Implicit multilinear modeling

The paper introduces a subclass of nonlinear differential-algebraic models of interest for applications. By restricting the nonlinearities to multilinear polynomials, it is possible to use modern tensor methods. This opens the door to new approximation and complexity reduction methods for large scale systems with relevant nonlinear behavior. The modeling procedures including composition, decomposition, normalization, and multilinearization steps are shown by an example of a local energy system with a nonlinear electrolyzer, a linear buck converter and a PI controller with saturation.