Hierarchical Stochastic Gradient and Hierarchical Multi‐Innovation Stochastic Gradient Identification for Multivariable ARX Models
Feng Ding, Yongsong Xiao, Ling Xu, Zhiming Fang
Abstract
ABSTRACT For an r‐input m‐output multivariable ARX system, it is commonly decomposed into m subsystems for identification. However, the corresponding identification algorithms incur a high computational burden because they fail to account for the coupling between variables within the subsystems. After parameterization, considering that all subsystem identification models share a common input information vector, we derive the coupled identification model for the entire system. Based on the obtained coupled identification model, this paper presents a hierarchical stochastic gradient identification algorithm and a hierarchical multi‐innovation stochastic gradient identification algorithm, and their variants for multivariable ARX systems. Finally, the simulation example is provided to show the effectiveness of the proposed algorithms.