Robust Identification Method for LPV ARX Systems and its Application to a Mechanical Unit

Xin Liu,Tingting Zhang,Xiaofeng Liu

doi:10.1109/access.2019.2952891

Xin Liu, Tingting Zhang + Show 1 more

Open Access

https://doi.org/10.1109/access.2019.2952891

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Abstract

This paper introduces a robust identification solution for the linear parameter varying Autoregressive Exogenous systems with outlier-contaminated outputs. The Laplace distribution with heavy tails and the expectation maximization algorithm are combined to build the robust system identification framework. To overcome the obstacles brought by the outliers, the Laplace distribution which can be decomposed into infinite Gaussian components, is applied to mathematically model the system noise. The problem of parameter estimation is solved using the expectation maximization algorithm, and the equations to infer the system model and noise parameters are simultaneously provided in the developed identification method. Finally, the verification tests performed on a numerical example and a mechanical unit are used to prove the validity of the developed identification method.

Highlights

Nowadays the higher requirement is proposed for system model with the fast development of the model-based control technologies, such as the robust control, the self-adaptive control, the back-stepping control and so on [1]–[7]
The valuable IV method was extended to the linear parameter varying (LPV) system identification and a refined instrumental variable (RIV) method was introduced
The comparison results with system outputs contaminated with 0% and 5% outliers are given in Figs. 8 and 9, respectively

Summary

INTRODUCTION

Nowadays the higher requirement is proposed for system model with the fast development of the model-based control technologies, such as the robust control, the self-adaptive control, the back-stepping control and so on [1]–[7]. The idea of multi-model method for LPV SI was discussed in [25], Jin et al chose the Autoregressive Exogenous (ARX) models as the sub-models to represent the system local dynamics, the system output was obtained with an exponential weight function. The global identification of LPV ARX systems with uncertain scheduling variables was considered in [22]. The main contributions of current work lie in: 1) A robust identification solution for the LPV ARX systems with outlier-contaminated outputs is developed; 2) The decomposition of the Laplace distribution is employed in the identification process which assures the robustness of the proposed solution for outliers; 3) The equations to infer the parameters are obtained using the EM algorithm and the validity of the proposed solution is proved.

PROBLEM FORMULATION WITH THE LAPLACE DISTRIBUTION

AN OVERHEAD CRANE

CONCLUSION