Synchronization of uncertain fractional-order chaotic systems with disturbance based on a fractional terminal sliding mode controller

Wang, Dongfeng; Zhang, Jinying; Wang, Xiaoyan

doi:10.1088/1674-1056/22/4/040507

Cited by 22 publications

(11 citation statements)

References 54 publications

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“…There is a wide variety of literature [24,[33][34][35][36][37] on. Research about finite-time synchronization in allusion to fractional-order chaotic system with hidden attractors, are quite limited.…”

Section: Finite-time Synchronization Of the Fractional-order System Wmentioning

confidence: 99%

Hidden Coexisting Attractors in a Fractional‐Order System without Equilibrium: Analysis, Circuit Implementation, and Finite‐Time Synchronization

Zheng

Liu

2019

Mathematical Problems in Engineering

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In this paper, a novel three-dimensional fractional-order chaotic system without equilibrium, which can present symmetric hidden coexisting chaotic attractors, is proposed. Dynamical characteristics of the fractional-order system are analyzed fully through numerical simulations, mainly including finite-time local Lyapunov exponents, bifurcation diagram, and the basins of attraction. In particular, the system can generate diverse coexisting attractors varying with different orders, which presents ample and complex dynamic characteristics. And there is great potential for secure communication. Then electronic circuit of the fractional-order system is designed to help verify its effectiveness. What is more, taking the disturbances into account, a finite-time synchronization of the fractional-order chaotic system without equilibrium is achieved and the improved controller is proven strictly by applying finite-time stable theorem. Eventually, simulation results verify the validity and rapidness of the proposed method. Therefore, the fractional-order chaotic system with hidden attractors can present better performance for practical applications, such as secure communication and image encryption, which deserve further investigation.

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Section: Finite-time Synchronization Of the Fractional-order System Wmentioning

confidence: 99%

Hidden Coexisting Attractors in a Fractional‐Order System without Equilibrium: Analysis, Circuit Implementation, and Finite‐Time Synchronization

Zheng

Liu

2019

Mathematical Problems in Engineering

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“…Suwat provided a feedback controller for the robust synchronization of fractional order unified chaotic systems based on the developed LMI stabilization condition [20]. Wang et al deliberated on the synchronization of uncertain fractional order chaotic systems with external disturbance by a fractional terminal sliding mode control [21]. And Aghababa considered the finite-time chaos synchronization of fractional order systems based on the fractional Lyapunov stability theorem [22].…”

Section: Introductionmentioning

confidence: 99%

Generalized Synchronization of Fractional Order Chaotic Systems with Time-Delay

Wang¹

2016

IJMEA

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Abstract:Generalized synchronization of time-delayed fractional order chaotic systems is investigated. According to the stability theorem of linear fractional differential systems with multiple time-delays, a nonlinear fractional order controller is designed for the synchronization of systems with identical and non-identical derivative orders. Both complete synchronization and projective synchronization also can be realized based on the proposed controller. The effectiveness and robustness of the controller are verified in the numerical simulations.

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“…It is worth studying. Until now, many synchronous strategies have been presented for the synchronization of fractional order chaos such as pinning synchronization [22], function projective synchronization [23], adaptive synchronization [24], and finite-time synchronization [25].…”

Section: Introductionmentioning

confidence: 99%

Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

Wang

Cao

Wang

et al. 2015

Mathematical Problems in Engineering

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This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI) interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D) chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.

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Synchronization of uncertain fractional-order chaotic systems with disturbance based on a fractional terminal sliding mode controller

Cited by 22 publications

References 54 publications

Hidden Coexisting Attractors in a Fractional‐Order System without Equilibrium: Analysis, Circuit Implementation, and Finite‐Time Synchronization

Hidden Coexisting Attractors in a Fractional‐Order System without Equilibrium: Analysis, Circuit Implementation, and Finite‐Time Synchronization

Generalized Synchronization of Fractional Order Chaotic Systems with Time-Delay

Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

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