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| A stochastic gradient-based two-step sparse identification algorithm formultivariate ARX systems |
| YanxinFu1,WenxiaoZhao1,2 |
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| (1 Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China) |
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| 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. |
| 关键词: ARX system · Stochastic gradient algorithm · Sparse identification · Support recovery · Parameter estimation · Strong consistency |
| DOI：https://doi.org/10.1007/s11768-024-00219-5 |
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| 基金项目: |
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| A stochastic gradient-based two-step sparse identification algorithm formultivariate ARX systems |
| Yanxin Fu1,Wenxiao Zhao1,2 |
| (1 Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China) |
| 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. |
| Key words: ARX system · Stochastic gradient algorithm · Sparse identification · Support recovery · Parameter estimation · Strong consistency |
