Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller

Aghababa, Mohammad Pourmahmood

doi:10.1016/j.cnsns.2011.10.028

Cited by 155 publications

(84 citation statements)

References 53 publications

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“…According to condition (23), the synchronization error is on the sliding surface at initial time. Therefore, synchronization exactly at a pre-specified time with complete robustness will be achieved if there is a controller that does not allow the synchronization error trajectory to deviate from the sliding surface ever so slightly, or equivalently keeping the switching surfaces (24) zero at all times.…”

Section: Controller Designmentioning

confidence: 99%

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A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

Khanzadeh

Pourgholi

2016

Nonlinear Dyn

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In this paper, attempts are made to design a novel time-varying switching surface in sliding mode control which enables us to synchronize two fractional chaotic systems precisely at any arbitrary pre-specified time. For both Caputo (C) and Riemann-Liuville (RL) derivatives, control laws based on Lyapunov stability theorem are derived. The proposed method is completely robust against existence of uncertainties and exogenous disturbances due to eliminating the reaching phase. Since the sign function is replaced by fractional RL integral of the sign function, the chattering is removed. The simulation results in different scenarios are reported to show the effectiveness of the proposed method.

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Section: Controller Designmentioning

confidence: 99%

“…In [19][20][21] a reaching law for the reaching phase is established, and synchronization in [22] has complete robustness due to the elimination of the reaching phase. In [23] and [24], sliding mode controllers guaranteeing the finite-time convergence to a sliding surface with asymptotical stability have been proposed.…”

mentioning

confidence: 99%

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

Khanzadeh

Pourgholi

2016

Nonlinear Dyn

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“…The other reason is that fractional controller has shown that it has more potential and more design freedom comparing to the standard integer order controller [18,25]. For more details on fractional calculus, please refer to [1,3,6,8,11,12,15,17,20,22,30].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations

Hanan¹,

Ahmad²,

Fadhel³

2017

J. Nonlinear Sci. Appl.

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This paper focuses on the application of fractional backstepping control scheme for nonlinear fractional partial differential equation (FPDE). Two types of fractional derivatives are considered in this paper, Caputo and the Grünwald-Letnikov fractional derivatives. Therefore, obtaining highly accurate approximations for this derivative is of a great importance. Here, the discretized approach for the space variable is used to transform the FPDE into a system of fractional differential equations. The convergence of the closed loop system is guaranteed in the sense of Mittag-Leffler stability. An illustrative example is given to demonstrate the effectiveness of the proposed control scheme.

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“…People have applied it to control chaos because it can drive the state which is not on the sliding surface to the steady state in limited time [25,26]. However, there are almost no relevant outcomes about sliding mode control for general class of 4-D fractional-order chaos.…”

Section: Introductionmentioning

confidence: 99%

Simplified Sliding Mode of a Novel Class of Four-dimensional Fractional-order Chaos

Wang¹,

Li²,

Zhu³

2015

IJCA

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Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller

Cited by 155 publications

References 53 publications

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations

Simplified Sliding Mode of a Novel Class of Four-dimensional Fractional-order Chaos

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