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 Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

Adaptive Synchronization of Fractional Hyper-Chaotic System with Unknown Parameters

2013 ◽  
Vol 850-851 ◽  
pp. 868-871 ◽  
Author(s):  
Li Xin Yang ◽  
Wan Sheng He ◽  
Jin Ping Jia ◽  
Fan Di Zhang
Keyword(s):  
Fractional Order ◽  
Tracking Control ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Fractional Systems ◽  
Control Approach ◽  
The Stability

In this paper, chaos synchronization of the modified Sprott E system is investigated. Based on the stability theorem for fractional systems, tracking control approach is used for the fractional-order systems with uncertain parameters. Meanwhile, suitable adaptive synchronization controller and recognizing rules of the uncertain parameters are designed. Numerical simulation results show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order hyper-chaotic systems.

DIVERSE STRUCTURE SYNCHRONIZATION OF FRACTIONAL ORDER HYPER-CHAOTIC SYSTEMS

2013 ◽  
Vol 27 (11) ◽  
pp. 1350034 ◽  
Author(s):  
XING-YUAN WANG ◽  
GUO-BIN ZHAO ◽  
YU-HONG YANG
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Rossler System ◽  
Rössler System ◽  
Predictor Corrector ◽  
Fractional Orders ◽  
Active Control Method

This paper studied the dynamic behavior of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system, then numerical analysis of the different fractional orders hyper-chaotic systems are carried out under the predictor–corrector method. We proved the two systems are in hyper-chaos when the maximum and the second largest Lyapunov exponential are calculated. Also the smallest orders of the systems are proved when they are in hyper-chaos. The diverse structure synchronization of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system is realized using active control method. Numerical simulations indicated that the scheme was always effective and efficient.

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.

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.

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