Sparse Identification of ARX Model Based on $L_{p}$–Regularization

This paper studies the sparse identification problem of ARX model by using the
$L_{p}$
-regularization method with
$0 < p < 1$
. We construct the information criterion which is a linear combination of the prediction error with the
$L_{p}$
- regularization term where the coefficient can be adaptively adjusted. By minimizing the information criterion, we propose a sparse parameter identification algorithm based on
$L_{p}$
-regularization. We design the adaptive step size by using the observations and obtain the parameter convergence and set convergence of the proposed algorithm. Finally, we give a simulation example to show that the
$L_{p}$
-regularization algorithm proposed in this paper has better performance than the
$L_{1}$
-regularization algorithm and the recursive least squares.