Enhanced kernels for nonparametric identification of a class of nonlinear systems

This paper deals with nonparametric nonlinear system identification via Gaussian process regression. We show that, when the system has a particular structure, the kernel recently proposed in [1] for nonlinear system identification can be enhanced to improve the overall modeling performance. More specifically, we modify the definition of the kernel by allowing different orders for the exogenous and the autoregressive parts of the model. We also show that all the hyperparameters can be estimated by means of marginal likelihood optimization. Numerical results on two benchmark simulation examples illustrate the effectiveness of the proposed approach.