Identification of Nonlinear State-Space Systems via Sparse Bayesian and Stein Approximation Approach

Limin Zhang (), Junpeng Li, Wenting Zhang and Junzi Yang
Additional contact information
Limin Zhang: College of Intelligence and Computing, Tianjin University, Tianjin 300072, China
Junpeng Li: Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China
Wenting Zhang: Department of Mathematics and Computer Science, Hengshui University, Hengshui 053000, China
Junzi Yang: Department of Mathematics and Computer Science, Hengshui University, Hengshui 053000, China

Mathematics, 2022, vol. 10, issue 19, 1-18

Abstract: This paper is concerned with the parameter estimation of non-linear discrete-time systems from noisy state measurements in the state-space form. A novel sparse Bayesian convex optimisation algorithm is proposed for the parameter estimation and prediction. The method fully considers the approximation method, parameter prior and posterior, and adds Bayesian sparse learning and optimization for explicit modeling. Different from the previous identification methods, the main identification challenge resides in two aspects: first, a new objective function is obtained by our improved Stein approximation method in the convex optimization problem, so as to capture more information of particle approximation and convergence; second, another objective function is developed with L 1 -regularization, which is sparse method based on recursive least squares estimation. Compared with the previous study, the new objective function contains more information and can easily mine more important information from the raw data. Three simulation examples are given to demonstrate the proposed algorithm’s effectiveness. Furthermore, the performances of these approaches are analyzed, including parameter estimation of root mean squared error ( RMSE ), parameter sparsity and prediction of state and output result.

Keywords: sparse Bayesian identification; state-space; convex optimisation; Stein approximation method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/19/3667/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/19/3667/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:19:p:3667-:d:934882

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().