A stochastic gradient-based two-step sparse identification algorithm formultivariate ARX systems

关键词:  ARX system · Stochastic gradient algorithm · Sparse identification · Support recovery · Parameter estimation · Strong consistency

Key words:  ARX system · Stochastic gradient algorithm · Sparse identification · Support recovery · Parameter estimation · Strong consistency

摘要:

We consider the sparse identification ofmultivariateARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.

Abstract:

We consider the sparse identification ofmultivariateARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.