Modified sliding mode synchronization of typical three-dimensional fractional-order chaotic systems

Gao, Lei; Wang, Zhihui; Zhou, Ke; Zhu, Wei; Wu, Zhiding; Ma, Tiedong

doi:10.1016/j.neucom.2015.04.031

Cited by 28 publications

(18 citation statements)

References 45 publications

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“…As can be seen from (18) , the fractional derivative of the Lyapunov function is negative semidefinite, then it can be concluded from Theorem 1 that the origin of system (16), (14) is uniformly stable, and therefore e 1 , e 2 , e 3 , φ ∈ L ∞ , and this concludes the proof.…”

Section: Lemma 2 (Adaptive Fractional Synchronization Using Control mentioning

confidence: 52%

“…Assuming that e 1 , e 2 , e 3 , φ are differentiable, then applying Lemma 1 to (17) and using (16) and (14) it can be written as…”

Section: Lemma 2 (Adaptive Fractional Synchronization Using Control mentioning

confidence: 99%

“…We can find some few works that can be applied to fractional Lorenz system, where only one control signal is used to make adaptive stabilization, using sliding mode control [15][16][17] . Applying these control techniques it is possible to stabilize a Lorenz system at the origin, using only one control signal.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters

Aguila‐Camacho

Duarte‐Mermoud

Aguilera

2016

Chaos, Solitons & Fractals

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This paper analyzes the synchronization of two fractional Lorenz systems in two cases: the first one considering fractional Lorenz systems with unknown parameters, and the second one considering known upper bounds on some of the fractional Lorenz systems parameters. The proposed control strategies use a reduced number of control signals and control parameters, employing mild assumptions. The stability of the synchronization errors is analytically demonstrated in all cases, and the convergence to zero of the synchronization errors is analytically proved in the case when the upper bounds on some system parameters are assumed to be known. Simulation studies are presented, which allows verifying the effectiveness of the proposed control strategies.CONICYT-Chile FB0809 FONDECYT 1150488 315000

show abstract

Section: Lemma 2 (Adaptive Fractional Synchronization Using Control mentioning

confidence: 52%

“…Assuming that e 1 , e 2 , e 3 , φ are differentiable, then applying Lemma 1 to (17) and using (16) and (14) it can be written as…”

Section: Lemma 2 (Adaptive Fractional Synchronization Using Control mentioning

confidence: 99%

See 1 more Smart Citation

Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters

Aguila‐Camacho

Duarte‐Mermoud

Aguilera

2016

Chaos, Solitons & Fractals

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“…However, from a pratical point of view, it is more valuable to stabilize fractional-order chaotic system in a given finite-time rather than merely asymptotically. Moreover, it has now been identified that finite-time stabilization of dynamics systems gives rise to a high-precision performance besides finite-time convergence to zero [37], [38]. The problem of finite-time chaotic synchronization using the nonsingular sliding mode surface was solved by [39].…”

Section: Introductionmentioning

confidence: 99%

Generalized finite-time function projective synchronization of two fractional-order chaotic systems via a modified fractional nonsingular sliding mode surface

Kengne¹,

Tchitnga²,

Fomethe³

et al. 2017

Communications in Numerical Analysis

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This paper addresses the problem of generalized finite-time function projective synchronization (GFFPS) of fractionalorder chaotic systems. A modified fractional nonsingular terminal sliding mode surface and an appropriate robust fractional sliding mode control law are proposed, taking into account the effects of model uncertainties and of the external disturbances. An appropriate Lyapunov functional candidate is used to prove the finite-time existence of the sliding motion. Compared with the existing nonsingular sliding mode surface, our sliding mode surface permits to reduce the settling time of synchronization. Finally, some numerical simulations taking into consideration the Gaussian white noise produced by the electrical line are presented to demonstrate the effectiveness and applicability of the proposed technique.

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“…Finite-time synchronization of uncertain fractional chaotic systems with disturbance has been accomplished by a fractional terminal sliding mode controller in [27]. Gao et al in [28] have utilized a modified sliding mode controller for the finite-time synchronization of typical threedimensional fractional chaotic systems. Mohadeszadeh and Delavari in [29] have proposed a novel adaptive sliding mode approach for the synchronization of fractional chaotic and hyper-chaotic systems with unknown parameters and model uncertainties and have proved its finite-time stability, as well.…”

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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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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Modified sliding mode synchronization of typical three-dimensional fractional-order chaotic systems

Cited by 28 publications

References 45 publications

Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters

Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters

Generalized finite-time function projective synchronization of two fractional-order chaotic systems via a modified fractional nonsingular sliding mode surface

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

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