Nonlinear system identification via Gaussian regression and mixtures of kernels

We present a novel nonparametric approach for identification of nonlinear systems. Exploiting the framework of Gaussian regression, the unknown nonlinear system is modeled as a realization from a Gaussian random field. Its autocovariance is a mixture of Gaussian kernels parametrized by few hyperparameters describing the interactions among past inputs and outputs. The kernel structure and unknown hyperparameters are estimated by maximizing their marginal likelihood. Then, the nonlinear model is obtained by solving a Tikhonov-type variational problem. The Hilbert space the estimate belongs to is characterized. Benchmarks problems taken from the literature demonstrate the effectiveness of the new approach.