Sparse augmented Lagrangian algorithm for system identification

A huge class of nonlinear dynamic systems can be approximated by the Nonlinear AutoRegressive with eXogenous inputs (NARX) models. This paper proposes a novel method, Sparse Augmented Lagrangian (SAL), for NARX model variable selection and parameter estimation. Firstly, Split Augmented Lagrangian Shrinkage Algorithm (SALSA) is applied to produce some intermediate models with subsampling technique, and then only the model terms with high selecting probability are chosen into the final model, followed by the model parameter estimation via SALSA. The model sparsity and algorithm convergence can be guaranteed through theoretical analysis. Two nonlinear examples and one real-world application from the process industry are used to demonstrate the effectiveness and advantages of the proposed method in comparison to several popular methods.