Multi-Innovation Stochastic Gradient Identification Algorithm for Hammerstein Controlled Autoregressive Autoregressive Systems Based on the Key Term Separation Principle and on the Model Decomposition

Huiyi Hu,Xiao Yongsong,Rui Ding

doi:10.1155/2013/596141

Huiyi Hu, Xiao Yongsong + Show 1 more

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https://doi.org/10.1155/2013/596141

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Journal: Journal of Applied Mathematics	Publication Date: Jan 1, 2013
Citations: 32	License type: CC BY 3.0

Affiliation: Jiangnan University

Abstract

An input nonlinear system is decomposed into two subsystems, one including the parameters of the system model and the other including the parameters of the noise model, and a multi-innovation stochastic gradient algorithm is presented for Hammerstein controlled autoregressive autoregressive (H-CARAR) systems based on the key term separation principle and on the model decomposition, in order to improve the convergence speed of the stochastic gradient algorithm. The key term separation principle can simplify the identification model of the input nonlinear system, and the decomposition technique can enhance computational efficiencies of identification algorithms. The simulation results show that the proposed algorithm is effective for estimating the parameters of IN-CARAR systems.

Highlights

There exist many nonlinear systems in process control [1,2,3]
In order to improve the convergence rate of the SG algorithm, Xiao et al presented a multi-innovation stochastic gradient parameter estimation algorithm for input nonlinear controlled autoregressive (IN-CAR) models using the over-parameterization method [19]; Chen et al proposed a modified stochastic gradient algorithm by introducing a convergence index in order to improve the convergence rate of the parameter estimation [20]; Han and Ding developed a multi-innovation stochastic gradient algorithm for multi-input single-output systems [21]; Liu et al studied the performance of the stochastic gradient algorithm for multivariable systems [22]
The paper focuses on the parameter estimation of a Hammerstein nonlinear controlled autoregressive autoregressive (H-CARAR) system, that is, an input nonlinear controlled autoregressive autoregressive (IN-CARAR) system, which consists of a nonlinear block and a linear dynamic subsystem

Summary

Introduction

There exist many nonlinear systems in process control [1,2,3]. A nonlinear system can be modeled by input nonlinear systems [4] and output nonlinear systems [5], input-output nonlinear systems [6], feedback nonlinear systems [7], and so on. In order to improve the convergence rate of the SG algorithm, Xiao et al presented a multi-innovation stochastic gradient parameter estimation algorithm for input nonlinear controlled autoregressive (IN-CAR) models using the over-parameterization method [19]; Chen et al proposed a modified stochastic gradient algorithm by introducing a convergence index in order to improve the convergence rate of the parameter estimation [20]; Han and Ding developed a multi-innovation stochastic gradient algorithm for multi-input single-output systems [21]; Liu et al studied the performance of the stochastic gradient algorithm for multivariable systems [22]. Ding divided a Hammerstein nonlinear system into two subsystems based on the Journal of Applied Mathematics model decomposition and presented a hierarchical multiinnovation stochastic gradient algorithm for Hammerstein nonlinear systems [25].

The System Identification Model

The Stochastic Gradient Algorithm

The Multi-Innovation Stochastic Gradient Algorithm

Conclusions