Parameter identification and synchronization of fractional-order chaotic systems

Yuan, Liguo; Yang, Qigui

doi:10.1016/j.cnsns.2011.04.005

Cited by 89 publications

(48 citation statements)

References 48 publications

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“…The Lyapunov function is 2 2 V s = . The following can be derived: As long as a proper k value is set and the error system is in line with Lyapunov stability theory after disturbance, the synchronization control method is effective.…”

Section: In Above Model Z1(ωt) Z2(ωt) Z3(ωt) Are the True Stamentioning

confidence: 99%

“…Fractional differential equations not only provide a novel mathematical tool, but further, more successful mathematical models of systems [1,2]. As research OPEN ACCESS regarding chaotic systems has continually intensified, an increasing number of control and synchronization methods specific to chaotic systems have been proposed, verified, and applied effectively [3].…”

Section: Introductionmentioning

confidence: 99%

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Sliding-Mode Synchronization Control for Uncertain Fractional-Order Chaotic Systems with Time Delay

Liu

Yang

2015

Entropy

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Specifically setting a time delay fractional financial system as the study object, this paper proposes a single controller method to eliminate the impact of model uncertainty and external disturbances on the system. The proposed method is based on the stability theory of Lyapunov sliding-mode adaptive control and fractional-order linear systems. The controller can fit the system state within the sliding-mode surface so as to realize synchronization of fractional-order chaotic systems. Analysis results demonstrate that the proposed single integral, sliding-mode control method can control the time delay fractional power system to realize chaotic synchronization, with strong robustness to external disturbance. The controller is simple in structure. The proposed method was also validated by numerical simulation.

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Section: In Above Model Z1(ωt) Z2(ωt) Z3(ωt) Are the True Stamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sliding-Mode Synchronization Control for Uncertain Fractional-Order Chaotic Systems with Time Delay

Liu

Yang

2015

Entropy

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show abstract

“…Synchronization, as one of the most important collective behaviors in complex dynamic networks, has been extensively studied [12][13][14][15][16]. Synchronization in complex networks plays a significant role in the fields of signal generator, image processing, engineering, etc.…”

Section: Introductionmentioning

confidence: 99%

Pinning and adaptive synchronization of fractional-order complex dynamical networks with and without time-varying delay

Wang

Ruan

et al. 2018

Adv Differ Equ

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The synchronization problem for a class of fractional-order complex dynamical networks with and without time-varying delay is investigated in this paper. By utilizing generalized Barbalat's lemma, Razumikhin-type stability theory and matrix inequality technique, some sufficient criteria ensuring synchronization under pinning control and pinning adaptive feedback control are derived. Finally, three numerical simulations are presented to demonstrate the effectiveness of the obtained results.

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“…However, PSO also has defects, such as low optimization efficiency and the tendency to be easily trapped in the local optimum when the problem dimension is too high [11]. Yuan and Yang combined PSO and active control theory to realize fractional-order chaotic system parameter identification and synchronous control [12]. Huang et al used PSO based on quantum parallel characteristics for the parameter identification of fractional-order Lorenz system and Chen system [13].…”

Section: Introductionmentioning

confidence: 99%

Sequential Parameter Identification of Fractional‐Order Duffing System Based on Differential Evolution Algorithm

Zhong

et al. 2017

Mathematical Problems in Engineering

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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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Parameter identification and synchronization of fractional-order chaotic systems

Cited by 89 publications

References 48 publications

Sliding-Mode Synchronization Control for Uncertain Fractional-Order Chaotic Systems with Time Delay

Sliding-Mode Synchronization Control for Uncertain Fractional-Order Chaotic Systems with Time Delay

Pinning and adaptive synchronization of fractional-order complex dynamical networks with and without time-varying delay

Sequential Parameter Identification of Fractional‐Order Duffing System Based on Differential Evolution Algorithm

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