Auxiliary Model-Based Multi-Innovation Fractional Stochastic Gradient Algorithm for Hammerstein Output-Error Systems

Chen Xu,Yawen Mao

doi:10.3390/machines9110247

Abstract

This paper focuses on the nonlinear system identification problem, which is a basic premise of control and fault diagnosis. For Hammerstein output-error nonlinear systems, we propose an auxiliary model-based multi-innovation fractional stochastic gradient method. The scalar innovation is extended to the innovation vector for increasing the data use based on the multi-innovation identification theory. By establishing appropriate auxiliary models, the unknown variables are estimated and the improvement in the performance of parameter estimation is achieved owing to the fractional-order calculus theory. Compared with the conventional multi-innovation stochastic gradient algorithm, the proposed method is validated to obtain better estimation accuracy by the simulation results.

Highlights

The accuracy of a system model affects the performance and safety of industrial control systems [1,2,3,4,5], and system identification is a theory and method for constructing mathematical model of systems and has been widely implemented in practice [6,7,8,9]
Several new system identification methods and theories have been developed for nonlinear models in the literature, including the least squares methods [19], the gradientbased methods [20], the iterative methods [21],the subspace identification methods [22], the hierarchical identification theory [23], the auxiliary model and the multi-innovation (MI) identification theories [24]
We study the identification problem of the Hammerstein output-error moving average (OEMA) systems, which have been less studied due to the difficulty in identification [39,40]

Summary

Introduction

The accuracy of a system model affects the performance and safety of industrial control systems [1,2,3,4,5], and system identification is a theory and method for constructing mathematical model of systems and has been widely implemented in practice [6,7,8,9]. By extending scalar innovation into innovation vectors, the MI identification theory was proposed to improve the convergence speed and estimation accuracy in [31], and the fractional-order calculus method was introduced to show that it can achieve more satisfactory performance in [32,33]. In [37], a fractional-order SG algorithm was designed to identify the Hammerstein nonlinear ARMAX systems by an improved fractional-order gradient method. Based on the identification model, the fractional-order SG algorithm is extended to the identification of Hammerstein OEMA systems and an auxiliary model-based multi-innovation fractional stochastic gradient (AM-MIFSG) algorithm is presented by the auxiliary model identification idea. This paper aims to present an AM-MIFSG algorithm for Hammerstein OEMA systems to improve the parameter estimation accuracy

The AM-MISG Algorithm

The AM-MIFSG Algorithm

Examples Consider the following Hammerstein OEMA system: yk

Conclusions