On Identification of Nonlinear ARX Models with Sparsity in Regressors and Basis Functions

摘要

We present techniques for minimal order, sparse identification of Nonlinear ARX models. We consider two notions of sparsity - in the number of regressors used and in the number of basis functions employed by their regressor-to-output maps. We propose two regularized formulations for the sparse estimation problem with the additional constraint on maximum lag. The estimation is performed using proximal gradient descent methods. A bootstrapping technique in regressor space is proposed for tuning the regularization hyperparameters. We then present an extension to the basic NARX structure that guarantees BIBO stability and thus helps improve the generalizability and long-term forecasting ability of the model. The extension exploits the atomic representation of linear systems, and the associated minimization technique, to identify model parameters under sparsity constraints.