Synchronization of fractional order chaotic systems using active control method

Agrawal, Saurabh; Srivastava, Mayank; Das, S.

doi:10.1016/j.chaos.2012.02.004

Cited by 164 publications

(59 citation statements)

References 43 publications

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“…The aim of this paper is to design a fractional-order nonsingular terminal fuzzy sliding mode controller to stabilize the error dynamic system (12). In other words, the goal of this paper is to synchronize the response system (4) and the drive system (5).…”

Section: Definitionmentioning

confidence: 99%

“…Therefore, the analysis and control/synchronization of fractional-order dynamical chaotic systems are important in both theory and practice. Up till now, many control/synchronization methods, such as active control [12], active sliding mode control [13], adaptive-impulsive control [14], fuzzy adaptive control [15], and generalized projective synchronization [16] and the references therein, have been successfully applied to control/synchronize the chaos of fractional-order chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of Two Fractional-Order Chaotic Systems via Nonsingular Terminal Fuzzy Sliding Mode Control

Song

Tejado

et al. 2017

Journal of Control Science and Engineering

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The synchronization of two fractional-order complex chaotic systems is discussed in this paper. The parameter uncertainty and external disturbance are included in the system model, and the synchronization of the considered chaotic systems is implemented based on the finite-time concept. First, a novel fractional-order nonsingular terminal sliding surface which is suitable for the considered fractional-order systems is proposed. It is proven that once the state trajectories of the system reach the proposed sliding surface they will converge to the origin within a given finite time. Second, in terms of the established nonsingular terminal sliding surface, combining the fuzzy control and the sliding mode control schemes, a novel robust single fuzzy sliding mode control law is introduced, which can force the closed-loop dynamic error system trajectories to reach the sliding surface over a finite time. Finally, using the fractional Lyapunov stability theorem, the stability of the proposed method is proven. The proposed method is implemented for synchronization of two fractional-order Genesio-Tesi chaotic systems with uncertain parameters and external disturbances to verify the effectiveness of the proposed fractional-order nonsingular terminal fuzzy sliding mode controller.

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Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Synchronization of Two Fractional-Order Chaotic Systems via Nonsingular Terminal Fuzzy Sliding Mode Control

Song

Tejado

et al. 2017

Journal of Control Science and Engineering

View full text Add to dashboard Cite

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“…Studies on chaos synchronization for the fractional order systems are just beginning to attract some attention due to its potential applications in secure communication and control processing. There are many different methods and strategies of fractional order continuous and discrete chaos synchronization have been developed such as activation feedback method, linear and nonlinear feedback synchronization [3,4,8,13,20,25,29], sliding mode control [12,16,22,23,30,34], adaptive control [1,2,5,9,14,21,33], and projective synchronization [10,17,24]. To the best of our knowledge, most of research efforts mentioned above have concentrated on studying the synchronization of fractional order chaotic systems whose models are identical, different.…”

Section: Introductionmentioning

confidence: 99%

Projective reduce order synchronization of fractional order chaotic systems with unknown parameters

Al-Sawalha¹

2017

J. Nonlinear Sci. Appl.

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This paper, mainly concerns the adaptive projective reduce order synchronization behavior of uncertain chaotic system. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the states of two chaotic and hyperchaotic systems asymptotically synchronized up to a desired identical and different scaling matrix. Numerical simulation results show that the proposed method is effective, convenient, and also faster for projective dual synchronization of chaotic and hyperchaotic systems.

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“…Due to its importance in wide ranging application areas a number of synchronization schemes and methods have been developed. These include, adaptive control [7,15,22,24,26,29,35], sliding mode control [12,17,31,34,36], linear active control technique [3,6,10,23], projective synchronization [2,11,19,28] and nonlinear active control [4,5]. Synchronization between different order chaotic oscillators can be found frequently in nature.…”

Section: Introductionmentioning

confidence: 99%

Reduced-order synchronization of fractional order chaotic systems with fully unknown parameters using modified adaptive control

Al-Sawalha¹,

Shoaib²

2016

J. Nonlinear Sci. Appl.

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A novel reduced-order adaptive controller is extended and developed to synchronize two different fractional order chaotic systems with different dimensions. Based upon the parameters modulation and the adaptive control techniques, we show that dynamical evolution of third-order fractional order chaotic system can be synchronized with the projection of a fourth-order fractional order chaotic system even though their parameters are unknown. The techniques are successfully applied to fractional order hyperchaotic Chen (4th-order) and fractional order chaotic Liu (3rd-order) systems. Theoretical analysis and numerical simulations are shown to verify the results.

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Synchronization of fractional order chaotic systems using active control method

Cited by 164 publications

References 43 publications

Synchronization of Two Fractional-Order Chaotic Systems via Nonsingular Terminal Fuzzy Sliding Mode Control

Synchronization of Two Fractional-Order Chaotic Systems via Nonsingular Terminal Fuzzy Sliding Mode Control

Projective reduce order synchronization of fractional order chaotic systems with unknown parameters

Reduced-order synchronization of fractional order chaotic systems with fully unknown parameters using modified adaptive control

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