Hierarchical Stochastic Gradient and Hierarchical Multi‐Innovation Stochastic Gradient Identification for Multivariable ARX Models

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.