On Sparse Nonlinear System Identification Using Orthogonal Matching Pursuit, Orthogonal Least Squares and LASSO

System identification, as a rich and vital discipline, provides a practical and general methodology and tool for quantitatively modelling the input-output relationships of dynamical systems. Sparse nonlinear system identification (SNSI), especially parametric sparse nonlinear system identification (PSNSI), is an important and vital field of research with a wide range of applications. This work is concerned with PSNSI and particular attention is paid to the assessment of three well-known mainstream sparse learning methods, namely, orthogonal least squares (OLS), orthogonal matching pursuit (OMP) and least absolute shrinkage and selection operator (LASSO). The performances of these methods are tested and evaluated through three case studies relating to PSNSI problems. The research results and findings of this work provide practical useful information and guidance for researchers to better choose or adapt methods when solving PSNSI problems.