An Atomic Norm Minimization Framework for Identification of Parameter Varying Nonlinear ARX Models

Abstract

We propose a generalization of the popular nonlinear ARX model structure by treating its parameters as varying over time. The parameters are considered generated by linear filters operating on the model’s regressors. The filters are expressed as a sum of atoms that are either sum of damped exponentials and sinusoids, or sinusoids with time varying frequencies. This form allows us to enforce stability of the parameter evolution as well as leverage the atomic norm minimization framework for inducing sparsity. It also facilitates easy incorporation of smoothness related priors that that making it possible to treat these models as nonlinear extensions of the familiar LPV models.