Lyapunov-based fractional-order controller design to synchronize a class of fractional-order chaotic systems

Li, Ruihong; Chen, Weisheng

doi:10.1007/s11071-013-1169-0

Cited by 41 publications

(21 citation statements)

References 39 publications

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Section: Introductionmentioning

confidence: 99%

“…The important and salient characteristics of chaotic systems include their extreme sensitivity to initial conditions, making the synchronisation of chaotic systems vital. The rapid increase in interest in fractional-order chaotic systems has manifested in investigations into the chaotic behavior of fractional-order horizontal platform systems (Aghababa, 2014) and in the proliferation of other published articles on these systems (Yin et al, 2013;Li and Chen, 2014;Li and Tong, 2013).During the past two decades, the control and synchronisation of fractional-order and integer-order chaotic systems have largely attracted scientists and researchers due to their potential applications in secure communications, biological systems, medicine, and other fields. For example, an active-control technique has been provided for the identical and non-identical synchronisation of fractional-order chaotic systems (Srivastava et al, 2014).…”

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confidence: 99%

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Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems

Noghredani

Balochian

2017

Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences.

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INTRODUCTIONThe broad field of chaos theory has been among the most interesting issues researchers have studied in recent decades. Concepts related to chaos theory and its related disciplines are employed in different fields, including medicine (Sarbaz et al., 2012;Aghababa and Borjkhani 2014;Provata et al., 2012), economics (Pan et al., 2012;Airaudo and Zanna, 2012), functioning of laser diodes (Banerjee et al., 2012;Gao, 2012), and mathematics (Hosseinalipour, 2013;Kupka, 2014). The control of chaos-related phenomena has attracted wide attention from many different kinds of researchers.Although the idea of fractional-order operators has a history as long as that of integer-order operators, interest in this field is expanding due to an increasing amount of attention from scientists and mathematicians. In recent decades, fractional-order operators have been the driving force behind an increasing number of investigations. With the development of studies in this area, practical and theoretical investigations into the application of fractional-order operators in engineering sciences have now become widespread in the academic community (Padula and Visioli, 2014;Pakzad et al., 2013;Tripathy et al., 2015a;Tripathy et al., 2015b). For example, fractional-order calculations have been applied in mechanical and electrical engineering, biology, economics, and mathematics, among other fields (Hernandez et al., 2014;Wang and Li, 2014;Cortes and Elejabarrieta, 2007).A chaotic system is a highly complex, dynamic nonlinear system. The important and salient characteristics of chaotic systems include their extreme sensitivity to initial conditions, making the synchronisation of chaotic systems vital. The rapid increase in interest in fractional-order chaotic systems has manifested in investigations into the chaotic behavior of fractional-order horizontal platform systems (Aghababa, 2014) and in the proliferation of other published articles on these systems (Yin et al., 2013;Li and Chen, 2014;Li and Tong, 2013).During the past two decades, the control and synchronisation of fractional-order and integer-order chaotic systems have largely attracted scientists and researchers due to their potential applications in secure communications, biological systems, medicine, and other fields. For example, an active-control technique has been provided for the identical and non-identical synchronisation of fractional-order chaotic systems (Srivastava et al., 2014). In a different application, function-projective synchronisations (FPS) of identical and non-identical modified finance systems (MFS) and the Shimizu-Morioka system (S-MS) have been studied via active control technique (Kareem et al., 2012). Fast projective synchronisation of fractional-order chaotic and reverse chaotic systems with its application to an affine cipher using date of birth (DOB) have also been reviewed (Muthukumar PROCEEDINGS OF THE LATVIAN ACADEMY OF SCIENCES. Section B, Vol. 71 (2017)

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems

Noghredani

Balochian

2017

Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences.

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“…The main advantage of FO controllers is the greater flexility in improving the robustness and control performance. It has motivated renewed interest in various fields of FO control [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems

et al. 2015

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In this paper, an adaptive sliding mode technique based on a fractional-order (FO) switching-type control law is designed to guarantee robust stability for uncertain 3D FO nonlinear systems. A novel FO switching-type control law is proposed to ensure the existence of the sliding motion in finite time. Appropriate adaptive laws are shown to tackle the uncertainty and external disturbance. The calculation formula of the reaching time is analyzed and computed. The reachability analysis is visualized to show how to obtain a shorter reaching time. A stability criterion of the FO sliding mode dynamics is derived based on indirect approach to Lyapunov stability. posed control scheme are illustrated through numerical simulations.

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“…Adaptive control is a reliable approach to overcome modeling imprecisions and external disturbances. Adaptive control schemes are widely used and its performance is validated in many engineering challenging problems such as chaos synchronization [39], control of DC motor [40], hard disk driver [41] and electro-hydraulic system [42] and many other problems available in literature.…”

Section: Introductionmentioning

confidence: 99%