Separable Synchronous Gradient‐Based Iterative Algorithms for the Nonlinear ExpARX System

Abstract

This article is aimed to study the parameter identification of the ExpARX system. To overcome the computational complexity associated with a large number of feature parameters, a parameter separation scheme based on the different features of the identification model is introduced. In terms of the phenomenon that the coupling parameters lead to the inability of algorithms, a separable synchronous interactive estimation method is introduced to eliminate the coupling parameters and perform parameter estimation in accordance with the hierarchical principle. For the purpose of achieving high‐accuracy performance and reducing complexity, a separable synchronous gradient iterative algorithm is derived by means of gradient search. In order to improve the identification accuracy, a separable synchronous multi‐innovation gradient iterative algorithm is proposed by introducing the multi‐innovation identification theory. In order to improve the convergence speed, a separable synchronous multi‐innovation conjugate gradient iterative algorithm is proposed by introducing the conjugate gradient theory. Finally, a simulation example and a real‐life example of piezoelectric ceramics are used to verify the effectiveness of the proposed algorithm.