Robust Standard Gradient Descent Algorithm for ARX Models Using Aitken Acceleration Technique

被引：19

作者：

Chen, Jing ^{[1
]}

Gan, Min ^{[2
]}

Zhu, Quanmin ^{[3
]}

Narayan, Pritesh ^{[3
]}

Liu, Yanjun ^{[4
]}

机构：

[1] Jiangnan Univ, Sch Sci, Wuxi 214122, Jiangsu, Peoples R China

[2] Qingdao Univ, Coll Comp Sci & Technol, Qingdao 266071, Peoples R China

[3] Univ West England, Dept Engn Design & Math, Bristol BS16 1QY, Avon, England

[4] Jiangnan Univ, Key Lab Adv Proc Control Light Ind, Minist Educ, Wuxi 214122, Jiangsu, Peoples R China

来源：

IEEE TRANSACTIONS ON CYBERNETICS | 2022年 / 52卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Convergence; Acceleration; Mathematical model; Standards; Parameter estimation; Nonlinear equations; Computational modeling; Aitken acceleration technique; ARX model; convergence rate; parameter estimation; standard gradient descent (SGD) algorithm; LINEAR-SYSTEMS; IDENTIFICATION;

D O I：

10.1109/TCYB.2021.3063113

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A robust standard gradient descent (SGD) algorithm for ARX models using the Aitken acceleration method is developed. Considering that the SGD algorithm has slow convergence rates and is sensitive to the step size, a robust and accelerative SGD (RA-SGD) algorithm is derived. This algorithm is based on the Aitken acceleration method, and its convergence rate is improved from linear convergence to at least quadratic convergence in general. Furthermore, the RA-SGD algorithm is always convergent with no limitation of the step size. Both the convergence analysis and the simulation examples demonstrate that the presented algorithm is effective.

引用

页码：9646 / 9655

页数：10

共 33 条

[1] Conjugate gradient method for fuzzy symmetric positive definite system of linear equations [J].

Abbasbandy, S ;

Jafarian, A ;

Ezzati, R .

APPLIED MATHEMATICS AND COMPUTATION, 2005, 171 (02) :1184-1191

[2] A blind approach to the Hammerstein-Wiener model identification [J].

Bai, EW .

AUTOMATICA, 2002, 38 (06) :967-979

[3] Convergence acceleration during the 20th century [J].

Brezinski, C .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 122 (1-2) :1-21

[4] A new Aitken type method for accelerating iterative sequences [J].

Bumbariu, Oana .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (01) :78-82

[5] Basis Function Matrix-Based Flexible Coefficient Autoregressive Models: A Framework for Time Series and Nonlinear System Modeling [J].

Chen, Guang-Yong ;

Gan, Min ;

Chen, C. L. Philip ;

Li, Han-Xiong .

IEEE TRANSACTIONS ON CYBERNETICS, 2021, 51 (02) :614-623

[6] Improved gradient descent algorithms for time-delay rational state-space systems: intelligent search method and momentum method [J].

Chen, Jing ;

Zhu, Quanmin ;

Hu, Manfeng ;

Guo, Liuxiao ;

Narayan, Pritesh .

NONLINEAR DYNAMICS, 2020, 101 (01) :361-373

[7] Multi-step-length gradient iterative algorithm for equation-error type models [J].

Chen, Jing ;

Ding, Feng ;

Liu, Yanjun ;

Zhu, Quanmin .

SYSTEMS & CONTROL LETTERS, 2018, 115 :15-21

[8] Modified stochastic gradient identification algorithms with fast convergence rates [J].

Chen, Jing ;

Ding, Feng .

JOURNAL OF VIBRATION AND CONTROL, 2011, 17 (09) :1281-1286

[9] System Identification Via Sparse Multiple Kernel-Based Regularization Using Sequential Convex Optimization Techniques [J].

Chen, Tianshi ;

Andersen, Martin S. ;

Ljung, Lennart ;

Chiuso, Alessandro ;

Pillonetto, Gianluigi .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2014, 59 (11) :2933-2945

[10] Decentralized Particle Filter With Arbitrary State Decomposition [J].

Chen, Tianshi ;

Schon, Thomas B. ;

Ohlsson, Henrik ;

Ljung, Lennart .

IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2011, 59 (02) :465-478

← 1 2 3 4 →