Construction of bilinear systems with nuclear norm regularization

In this paper, a method that constructs bilinear systems from input-output data in the time-domain is presented. A nuclear norm heuristic is employed to tackle the case of noisy data and to build a linear model. This mitigates the challenge of calculating the Markov parameters through noisy data for linear identification. Then, if needed, the order of the linear model can be reduced by using model reduction techniques. Finally, a least squares problem and a nonlinear optimization step are solved to add the nonlinear (bilinear) term and enrich the structure of the learned system. The applicability of the method is demonstrated on an industrial dataset of a heat exchanger experiment.