Stabilization of a class of fractional order chaotic systems via backstepping approach

Shukla, Manoj Kumar; Sharma, Bharat Bhushan

doi:10.1016/j.chaos.2017.03.011

Cited by 49 publications

(30 citation statements)

References 33 publications

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“…For example, the control fractional-order ferroresonance system, which can show chaotic phenomenon, was considered in paper [10] by using the adaptive backstepping control. Papers [11,12] investigated the stabilization and synchronization of a class of fractional-order chaotic systems via backstepping approach. Paper [13] proposed a new chaotic system with no equilibrium point and discussed its fractional-order backstepping control.…”

Section: Introductionmentioning

confidence: 99%

Robust Control and Synchronization of 3‐D Uncertain Fractional‐Order Chaotic Systems with External Disturbances via Adding One Power Integrator Control

Luo

Huang

2019

Complexity

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This paper investigates the control and synchronization of a class of 3-D uncertain fractional-order chaotic systems with external disturbances. The adding one power integrator control scheme, which is the generalization of the traditional backstepping method, is used to investigate the global stability of the control and synchronization manifold. As a result, several criteria for chaos control and synchronization are obtained. Compared with the previous results, the presented strategies can not only be applied to a class of strict-feedback systems but also be applied to more general class of fractional-order chaotic systems. In addition, the proposed controllers are robust against uncertain parameters and external disturbances. To validate the effectiveness of the proposed criteria, two illustrative examples are given.

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Section: Introductionmentioning

confidence: 99%

Robust Control and Synchronization of 3‐D Uncertain Fractional‐Order Chaotic Systems with External Disturbances via Adding One Power Integrator Control

Luo

Huang

2019

Complexity

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“…Especially, stabilization problem of fractional-order systems is a very interesting and important research topic. In recent years, more and more researchers and scientists have begun to address this problem [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. With the help of the Lyapunov direct method, Mittag-Leffler stability and generalized Mittag-Leffler stability was studied [10,20].…”

Section: Introductionmentioning

confidence: 99%

“…Necessary and sufficient conditions on the asymptotic stability of the positivity continuous time fractional-order systems with bounded time-varying delays are investigated by the monotonic and asymptotic property [14]. The stabilization problem of a class of fractional-order chaotic systems have been addressed [12]. Pseudo-state stabilization problem of fractional-order nonlinear systems has attracted the attention of some researchers [7-9, 13, 16].…”

Section: Introductionmentioning

confidence: 99%

Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients

Wang

2018

Adv Differ Equ

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In this paper, we consider the problem of Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients. With the help of backstepping design method, the stabilizing functions and tuning functions are constructed. The controller is designed to ensure that the pseudo-state of the fractional-order nonlinear system converges to the equilibrium. The effectiveness of the proposed method has been verified by some simulation examples.

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“…Another fractional-order chaotic systems were described in other works. [37][38][39] Khalil et al 40 proposed an interesting definition of derivative, this novel operator called conformable fractional derivative generalizes the classical concept of derivative. This derivative is well behaved and obeys the Leibniz rule and chain rule.…”

Section: Introductionmentioning

confidence: 99%

Fractional conformable attractors with low fractality

Morales‐Delgado

Gómez‐Aguilar

Escobar-Jiménez

2018

Math Methods in App Sciences

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In this paper, we considered a fractional conformable derivative of Liouville-Caputo type of fractional-order = n − , which contains a small perturbation and positive integer n values between [0;1] to obtain the solutions of three different fractional conformable attractors (Chen's attractor, Genesio-Tesi's attractor, and Liu's attractor). The fractional conformable Adomian decomposition method is applied to obtain an expansion of the fractional conformable derivative in = n − . The solutions of the fractional chaotic systems are calculated in the form of convergent series. We investigate the dynamics of these attractors by numerical simulations for different fractional orders values and parameter . KEYWORDSadomian decomposition method, chaos, fractional calculus, fractional conformable derivative, low-fractality 6378

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Stabilization of a class of fractional order chaotic systems via backstepping approach

Cited by 49 publications

References 33 publications

Robust Control and Synchronization of 3‐D Uncertain Fractional‐Order Chaotic Systems with External Disturbances via Adding One Power Integrator Control

Robust Control and Synchronization of 3‐D Uncertain Fractional‐Order Chaotic Systems with External Disturbances via Adding One Power Integrator Control

Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients

Fractional conformable attractors with low fractality

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