Online Identification of Uncertain Fractional-Order Nonlinear Systems Using a Reinforced Differential Evolution Optimizer

2019 ◽  
Author(s):  
Jiamin Wei ◽  
Yongguang Yu ◽  
YangQuan Chen
Keyword(s):  
Differential Evolution ◽  
Parameter Identification ◽  
Fractional Order ◽  
High Efficiency ◽  
Problem Formulation ◽  
Unknown Parameters ◽  
Online Identification ◽  
Adaptive Differential Evolution ◽  
Efficiency And Effectiveness ◽  
Hyperchaotic Systems

Abstract Parameter identification as known as a significant issue is investigated in this paper. The research focus on online identifying unknown parameters of uncertain fractional-order chaotic and hyperchaotic systems, which shows great potential in recent applications. Up to now, most of the existing online identification methods only focus on integer-order systems, thus, it’s necessary to expand these fundamental results to uncertain fractional-order nonlinear dynamic systems and adopt an effective optimizer to deal with the model uncertainties. Motivated by this consideration, this research introduces an efficient optimizer to offline and online parameter identification of the fractional-order chaotic and hyperchaotic systems through non-Lyapunov way. For problem formulation, a multi-dimensional optimization problem is converted into from the problem of parameter identification, where both systematic parameters and fractional derivative orders are considered as independent unknown parameters to be estimated. The experimental results illustrate that SHADE is significantly superior to the other compared approaches. In this case, online identification is conducted via SHADE, the simulation results further indicate that success-history based adaptive differential evolution (SHADE) algorithm is capable of detecting and determining the variations of parameters in uncertain fractional-order chaotic and hyperchaotic systems, and also is supposed to be a successful and potentially promising method for handling the online identification problems with high efficiency and effectiveness.

A systematic identification approach for biaxial piezoelectric stage with coupled Duhem-type hysteresis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Qun Chen ◽  
Zong-Xiao Yang ◽  
Zhumu Fu
Keyword(s):  
Parameter Identification ◽  
High Efficiency ◽  
Full Range ◽  
Unknown Parameters ◽  
Content Type ◽  
De Algorithm ◽  
Complicated Model ◽  
Identification Approach ◽  
Cross Axis ◽  
Systematic Identification

Purpose The problem of parameter identification for biaxial piezoelectric stages is still a challenging task because of the existing hysteresis, dynamics and cross-axis coupling. This study aims to find an accurate and systematic approach to tackle this problem. Design/methodology/approach First, a dual-input and dual-output (DIDO) model with Duhem-type hysteresis is proposed to depict the dynamic behavior of the biaxial piezoelectric stage. Then, a systematic identification approach based on a modified differential evolution (DE) algorithm is proposed to identify the unknown parameters of the Duhem-type DIDO model for a biaxial piezostage. The randomness and parallelism of the modified DE algorithm guarantee its high efficiency. Findings The experimental results show that the characteristics of the biaxial piezoelectric stage can be identified with adequate accuracy based on the input–output data, and the peak-valley errors account for 2.8% of the full range in the X direction and 1.5% in the Y direction. The attained results validated the correctness and effectiveness of the presented identification method. Originality/value The classical DE algorithm has many adjustment parameters, which increases the inconvenience and difficulty of using in practice. The parameter identification of Duhem-type DIDO piezoelectric model is rarely studied in detail and its successful application based on DE algorithm on a biaxial piezostage is hitherto unexplored. To close this gap, this work proposed a modified DE-based systematic identification approach. It not only can identify this complicated model with more parameters, but also has little tuning parameters and thus is easy to use.

scholarly journals Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 304-313 ◽  
Author(s):  
M. Mossa Al-Sawalha ◽  
Ayman Al-Sawalha
Keyword(s):  
Adaptive Control ◽  
Dynamical Systems ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Adaptive Laws ◽  
Analytic Expression ◽  
Hyperchaotic Systems

AbstractThe objective of this article is to implement and extend applications of adaptive control to anti-synchronize different fractional order chaotic and hyperchaotic dynamical systems. The sufficient conditions for achieving anti–synchronization are derived by using the Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. Theoretical analysis and numerical simulations are shown to verify the results.

Identification of Uncertain Incommensurate Fractional-Order Chaotic Systems Using an Improved Quantum-Behaved Particle Swarm Optimization Algorithm

2018 ◽  
Vol 13 (5) ◽  
Author(s):  
Jiamin Wei ◽  
Yongguang Yu ◽  
Di Cai
Keyword(s):  
Particle Swarm Optimization ◽  
Fractional Derivative ◽  
Parameter Identification ◽  
Fractional Order ◽  
Optimization Problem ◽  
Chaotic Systems ◽  
Particle Swarm ◽  
Unknown Parameters ◽  
Swarm Optimization ◽  
Systems Simulation

This paper is concerned with a significant issue in the research of nonlinear science, i.e., parameter identification of uncertain incommensurate fractional-order chaotic systems, which can be essentially formulated as a multidimensional optimization problem. Motivated by the basic particle swarm optimization and quantum mechanics theories, an improved quantum-behaved particle swarm optimization (IQPSO) algorithm is proposed to tackle this complex optimization problem. In this work, both systematic parameters and fractional derivative orders are regarded as independent unknown parameters to be identified. Numerical simulations are conducted to identify two typical incommensurate fractional-order chaotic systems. Simulation results and comparisons analyses demonstrate that the proposed method is suitable for parameter identification with advantages of high effectiveness and efficiency. Moreover, we also, respectively, investigate the effect of systematic parameters, fractional derivative orders, and additional noise on the optimization performances. The corresponding results further validate the superior searching capabilities of the proposed algorithm.

scholarly journals Adaptive synchronization of a class of fractional order chaotic system with uncertain parameters

2015 ◽  
Vol 11 (6) ◽  
pp. 5306-5316
Author(s):  
De-fu Kong
Keyword(s):  
Parameter Identification ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Stability Criterion ◽  
Local Stability ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Control Scheme

In this manuscript, the adaptive synchronization of a class of fractional order chaotic system with uncertain parameters is studied. Firstly, the local stability of the fractional order chaotic system is analyzed using fractional stability criterion. Then, based on the J function criterion, suitable adaptive synchronization controller and parameter identification rules of the unknown parameters are investigated. Finally, the numerical simulations are presented to verify the effectiveness and robustness of the proposed control scheme.

scholarly journals Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Fei Gao ◽  
Xue-Jing Lee ◽  
Heng-qing Tong ◽  
Feng-xia Fei ◽  
Hua-ling Zhao
Keyword(s):  
Differential Evolution ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Cuckoo Search ◽  
Unknown Parameters ◽  
Independent Variables ◽  
Novel Approach ◽  
Proper Translation ◽  
Fractional Orders ◽  
Identification Mechanism

In this paper, a non-Lyapunov novel approach is proposed to estimate the unknown parameters and orders together for noncommensurate and hyper fractional chaotic systems based on cuckoo search oriented statistically by the differential evolution (CSODE). Firstly, a novel Gaos’ mathematical model is proposed and analyzed in three submodels, not only for the unknown orders and parameters’ identification but also for systems’ reconstruction of fractional chaos systems with time delays or not. Then the problems of fractional-order chaos’ identification are converted into a multiple modal nonnegative functions’ minimization through a proper translation, which takes fractional-orders and parameters as its particular independent variables. And the objective is to find the best combinations of fractional-orders and systematic parameters of fractional order chaotic systems as special independent variables such that the objective function is minimized. Simulations are done to estimate a series of noncommensurate and hyper fractional chaotic systems with the new approaches based on CSODE, the cuckoo search, and Genetic Algorithm, respectively. The experiments’ results show that the proposed identification mechanism based on CSODE for fractional orders and parameters is a successful method for fractional-order chaotic systems, with the advantages of high precision and robustness.

scholarly journals Sequential Parameter Identification of Fractional-Order Duffing System Based on Differential Evolution Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Li Lai ◽  
Yuan-Dong Ji ◽  
Su-Chuan Zhong ◽  
Lu Zhang
Keyword(s):  
Differential Evolution ◽  
Parameter Identification ◽  
Fractional Order ◽  
Dynamic Properties ◽  
Differential Evolution Algorithm ◽  
Duffing System ◽  
Identification Method ◽  
System A ◽  
Evolution Algorithm ◽  
Search Capability

Using the dynamic properties of fractional-order Duffing system, a sequential parameter identification method based on differential evolution optimization algorithm is proposed for the fractional-order Duffing system. Due to the step by step parameter identification method, the dimension of parameter identification of each step is greatly reduced and the search capability of the differential evolution algorithm has been greatly improved. The simulation results show that the proposed method has higher convergence reliability and accuracy of identification and also has high robustness in the presence of measurement noise.

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