NEURAL NETWORK METHOD FOR PARAMETER ESTIMATION OF FRACTIONAL DISCRETE-TIME UNIFIED SYSTEMS

被引：2
作者：
Wu, Zhi-Qiang [1 ]
Wu, Guo-Cheng [1 ]
Zhu, Wei [1 ]
机构：
[1] Chongqing Univ Posts & Telecommun, Key Lab Intelligent Anal & Decis Complex Syst, Chongqing 400065, Peoples R China
来源：
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2024年 / 32卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Fractional Unified System; Parameter Estimation; Neural Network; Deep Learning; CHAOTIC SYSTEMS; IDENTIFICATION;
D O I：
10.1142/S0218348X2450004X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Data-driven learning of the fractional discrete-time unified system is studied in this paper. A neural network method is suggested in the parameter estimation of fractional discrete-time chaotic systems. An optimization problem is obtained and the famous Adam algorithm is employed to train the neural network's weights and parameters. The parameter estimation result is compared with that of the stepwise response sensitivity approach (SRSA). This paper provides a high accuracy method for parameter inverse problems. The method also can be applied to data-driven learning of other fractional chaotic systems.
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页数：8
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共 25 条
  • [1] On Riemann and Caputo fractional differences
    Abdeljawad, Thabet
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (03) : 1602 - 1611
  • [2] Neural Network Solution of Single-Delay Differential Equations
    Fang, Jie
    Liu, Chenglian
    Simos, T. E.
    Famelis, I. Th.
    [J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2020, 17 (01)
  • [3] Goodrich C., 2015, Discrete fractional calculus
  • [4] Parameter estimation for chaotic systems by particle swarm optimization
    He, Qie
    Wang, Ling
    Liu, Bo
    [J]. CHAOS SOLITONS & FRACTALS, 2007, 34 (02) : 654 - 661
  • [5] Neural network solution of pantograph type differential equations
    Hou, Chih-Chun
    Simos, Theodore E.
    Famelis, Ioannis Th.
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (06) : 3369 - 3374
  • [6] Parameter estimation of fractional-order arbitrary dimensional hyperchaotic systems via a hybrid adaptive artificial bee colony algorithm with simulated annealing algorithm
    Hu, Wei
    Yu, Yongguang
    Gu, Wenjuan
    [J]. ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE, 2018, 68 : 172 - 191
  • [7] Kilbas A. A., 2006, N HOLLAND MATH STUDI, V204, DOI DOI 10.1016/S0304-0208(06)80001-0
  • [8] Kingma DP., 2014, ARXIV, DOI DOI 10.48550/ARXIV.1412.6980
  • [9] MODELING AFTERSHOCKS BY FRACTIONAL CALCULUS: EXACT DISCRETIZATION VERSUS APPROXIMATE DISCRETIZATION
    Kong, Hua
    Yang, Guang
    Luo, Cheng
    [J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2021, 29 (08)
  • [10] An effective hybrid PSOSA strategy for optimization and its application to parameter estimation
    Li, Ling-lal
    Wang, Ling
    Liu, Li-heng
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 179 (01) : 135 - 146
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