Hierarchical Least Squares Identification for the Multivariate Input Nonlinear Controlled Autoregressive Moving Average Systems

• Published in: International journal of adaptive control and signal processing Vol. 39; no. 6; pp. 1174 - 1192
• Main Authors: Qiu, Fang, Wang, Lei, Mu, Wenying, Ji, Yan
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.06.2025
• Subjects: Algorithms; Autoregressive moving average; Estimation; Multivariate analysis; Nonlinear control; Nonlinear systems; Parameters; Subsystems
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.4000

This article presents a decomposition‐based least squares estimation algorithm for the multivariate input nonlinear system. By using the hierarchical identification principle, the algorithm breaks down a nonlinear system into two subsystems, one containing the parameters of the linear dynamic block and the other containing the parameters of the nonlinear static block. Treating the unknown variables contained in the information vector of the model is to replace them with the outputs of an auxiliary model. The comparative results between the hierarchical recursive algorithm developed in this article and the recursive least squares algorithm are provided to test the proposed algorithms have lower computational cost and the higher estimation accuracy. Furthermore, the convergence of the hierarchical recursive algorithm is analyzed, which can guarantee the stability of the algorithm. The simulation results confirm the efficacy of the derived algorithm in effectively estimating the parameters of the nonlinear systems.