Adaptive synchronisation of fractional-order chaotic systems

张若洵,; 杨世平,

doi:10.1088/1674-1056/19/2/020510

Cited by 33 publications

(2 citation statements)

References 22 publications

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“…In [10] and [11], the synchronization of chaotic systems based on an observer design has been studied. In [12][13][14][15], the adaptive control method has also been utilized for fractional chaos synchronization.…”

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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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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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“…Various types of systems have been studied, such as the Rössler system [13], the modified Duffing fractional order system [14], and the Chen and Lu systems [15], among others. In the case of non-adaptive synchronization of fractional order systems some solutions have been proposed [16]- [18], but in the adaptive case, we only have a few studies [19], [20], and a complete theoretical solution does not exist to date.…”

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confidence: 99%

Adaptive synchronization of fractional order systems of the Lorenz type

Aguilera

Duarte‐Mermoud

2011

2011 9th IEEE International Conference on Control and Automation (ICCA)

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This paper presents the synchronization analysis of two fractional order systems of the Lorenz type, with unknown parameters. The study was done through simulations in order to understand the mechanisms involved in this synchronization process for later use in the derivation of analytical techniques. The study includes adaptive synchronization between two fractional order systems of the Lorenz type using integer and fractional adaptive laws. Simulation results are shown for the synchronization of integer systems with fractional adaptive laws, and for the synchronization of fractional order systems with integer and fractional adaptive laws.

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Synchronization of fractional-order chaotic systems using unidirectional adaptive full-state linear error feedback coupling

Leung

Chu

et al. 2015

Nonlinear Dyn

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Based on the stability theory of fractionalorder system, a novel unidirectional adaptive full-state linear error feedback coupling scheme is extended to control and synchronize all of fractional-order differential (FOD) chaotic systems with in-commensurate (and commensurate) orders. The feedback strength is adaptive to an updated law rather than prescribed as a constant. The convergence speed of feedback strength is regulated by a constant. With rigorous linear algebraic theorems and precisely numerical matrix computations, a reasonable interval in which the ultimate final control strength dwells is suggested, and the reliability of synchronization state is guaranteed. It demonstrates that the unidirectional full-state linear feedback coupling scheme can be adopted to control and synchronize FOD chaotic systems directly. Numerical simulations of three representative FOD chaotic systems illustrate the effectiveness of the proposed scheme.

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Adaptive synchronisation of fractional-order chaotic systems

Cited by 33 publications

References 22 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

Adaptive synchronization of fractional order systems of the Lorenz type

Synchronization of fractional-order chaotic systems using unidirectional adaptive full-state linear error feedback coupling

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