Two‐stage gradient‐based iterative algorithms for the fractional‐order nonlinear systems by using the hierarchical identification principle

Abstract

Summary This article focuses on the parameter estimation issues for a fractional‐order nonlinear system with autoregressive noise. In the process, the challenge and difficulty are to identify the parameters of the system as well as the order. To reduce the complexity of the structure, we split the system into two subsystems by utilizing the hierarchical identification principle and derive a two‐stage gradient‐based iterative (2S‐GI) algorithm by minimizing two criterion functions. Compared with the calculation amount of the gradient‐based iterative algorithm, the computation of the 2S‐GI algorithm is significantly reduced. Moreover, in order to improve the identification accuracy, we propose a two‐stage moving‐data‐window gradient‐based iterative algorithm. Finally, the simulation examples test the effectiveness of the proposed algorithms.