Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control

Deepika, Deepika; Kaur, Sandeep; Narayan, Shiv

doi:10.1016/j.chaos.2018.07.028

Cited by 39 publications

(24 citation statements)

References 43 publications

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“…The state variables of the response system (35) and and the states variables of (xyz) projection of the drive system (34) can be synchronized asymptotically and globally for all initial conditions using the control law (38) and the adaptive parameter update laws (39).…”

Section: Theoremmentioning

confidence: 99%

“…The uncertain parameters are set to a 1 = 10, b 1 = 28, c 1 = 8/3, a 2 = 10, b 2 = 28, c 2 = 8/3. The initial values of the fractional-order drive and response systems (34)- (35) and the estimated parameters are, respectively, and arbitrarily set in simulations to x 1 (0) = 12, y 1 (0) = 22, z 1 (0) = 31, w 1 (0) = 4, x 2 (0) = 0, y 2 (0) = 1, and z 2 (0) = 2 andã 1 (0) = 10, b 1 (0) = 10,c 1 (0) = 10,ã 2 (0) = 10,b 2 (0) = 10 andc 2 (0) = 10. Figures 1-2 depict the mod- ified adaptive sliding-mode synchronization of systems (34)- (35) via the adaptive control laws (38) and (39).…”

Section: Theoremmentioning

confidence: 99%

“…Nowadays, after the pioneering work of Pecora and Carroll [17], various types of chaos synchronization such as complete synchronization [18,19], phase synchronization [20,21], generalized synchronization [22,23], lag synchronization [24,25] projective synchronization [26,27], Q-S synchronization [28], amplitude envelope synchronization [29], anticipated and lag synchronization [30,31] have been described. There are many methods of synchronization, such as the active control, adaptive control, linear or nonlinear feedback control, and sliding mode control [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. The fractional-order of the chaotic systems effects the transient performance of the chaotic synchronization, it has been investigated that the error in the synchronization of fractional-order systems decreases if the fractional order is increased.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of different order fractional-order chaotic systems using modify adaptive sliding mode control

Al-Sawalha

2020

Adv Differ Equ

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This paper proposes a modified adaptive sliding-mode control technique and investigates the reduced-order and increased-order synchronization between two different fractional-order chaotic systems using the master and slave system synchronization arrangement. The parameters of the master and slave systems are different and uncertain. These systems exhibit different chaotic behavior and topological properties. The dynamic behavior of the proposed synchronization schemes is more complex and unpredictable. These attributes of the proposed synchronization schemes enhance the security of the information signal in digital communication systems. The proposed switching law ensures the convergence of the error vectors to the switching surface and the feedback control signals guarantee the fast convergence of the error vectors to the origin. Lyapunov stability theory proves the asymptotic stability of the closed-loop. The paper also designs suitable parameters update laws the estimate the unknown parameters. Computer-based simulation results verify the theoretical findings.

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Section: Theoremmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Synchronization of different order fractional-order chaotic systems using modify adaptive sliding mode control

Al-Sawalha

2020

Adv Differ Equ

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“…New results on adaptive synchronisation design for chaotic Arneodo system of incommensurate fractional order with unknown parameters based on the Lyapunov stability theory were introduced in [8]. The finite time robust synchronisation problem of a class of uncertain fractional chaotic/hyper-chaotic systems with a novel fractional sliding mode control technique was investigated in [9]. A novel fractional-order fuzzy sliding mode control strategy was developed to realise the deployment of the tethered satellite system (TSS) with input saturation in [10].…”

Section: Introductionmentioning

confidence: 99%

Synchronisation of two different uncertain fractional-order chaotic systems with unknown parameters using a modified adaptive sliding-mode controller

Almatroud

2020

Adv Differ Equ

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This article investigates a modified adaptive sliding-mode controller to achieve synchronisation between two different fractional-order chaotic systems with fully unknown parameters. A suitable parameter updating law is designed to tackle the unknown parameters. For constructing the modified adaptive sliding-mode control, a simple sliding surface is designed and the stability of the suggested method is proved using Lyapunov stability theory. Finally, the proposed method is applied to gain chaos synchronisation between two different pairs of fractional-order chaotic systems with uncertain parameters. Numerical simulations are performed to demonstrate the robustness and efficiency of the proposed method.

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“…Shukla and Sharma designed a backstepping controller and analyzed the stability of the designed controller for a class of three-dimensional chaotic systems [ 24 ]. To name just a few, fuzzy controller [ 25 , 26 , 27 , 28 , 29 ], sliding mode controller [ 30 , 31 , 32 , 33 , 34 ], and hybrid controllers [ 35 , 36 , 37 , 38 , 39 ] are some other controllers that are implemented to control and synchronize the chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Entropy Analysis and Neural Network-Based Adaptive Control of a Non-Equilibrium Four-Dimensional Chaotic System with Hidden Attractors

Jahanshahi

Shahriari-kahkeshi

Alcaraz

et al. 2019

Entropy

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Today, four-dimensional chaotic systems are attracting considerable attention because of their special characteristics. This paper presents a non-equilibrium four-dimensional chaotic system with hidden attractors and investigates its dynamical behavior using a bifurcation diagram, as well as three well-known entropy measures, such as approximate entropy, sample entropy, and Fuzzy entropy. In order to stabilize the proposed chaotic system, an adaptive radial-basis function neural network (RBF-NN)–based control method is proposed to represent the model of the uncertain nonlinear dynamics of the system. The Lyapunov direct method-based stability analysis of the proposed approach guarantees that all of the closed-loop signals are semi-globally uniformly ultimately bounded. Also, adaptive learning laws are proposed to tune the weight coefficients of the RBF-NN. The proposed adaptive control approach requires neither the prior information about the uncertain dynamics nor the parameters value of the considered system. Results of simulation validate the performance of the proposed control method.

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Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control

Cited by 39 publications

References 43 publications

Synchronization of different order fractional-order chaotic systems using modify adaptive sliding mode control

Synchronization of different order fractional-order chaotic systems using modify adaptive sliding mode control

Synchronisation of two different uncertain fractional-order chaotic systems with unknown parameters using a modified adaptive sliding-mode controller

Entropy Analysis and Neural Network-Based Adaptive Control of a Non-Equilibrium Four-Dimensional Chaotic System with Hidden Attractors

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