Adaptive control and synchronization of a fractional-order chaotic system

Li, Chunlai; Tong, Yaonan

doi:10.1007/s12043-012-0500-5

Cited by 40 publications

(26 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Yet, several authors are also interested in the synchronization of the fractional-order a e-mail: g.litak@pollub.pl chaotic systems [22,23,[26][27][28][29][30][31][32][33][34][35]. The transient time preceding the synchronization state of chaotic oscillators is crucial as it unfortunately corresponds to the laps of time during which the encoded message cannot be recovered or sent.…”

Section: Introductionmentioning

confidence: 99%

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

et al. 2017

View full text Add to dashboard Cite

Abstract. The problem of finite-time synchronization of fractional-order simplest two-component chaotic oscillators operating at high frequency and application to digital cryptography is addressed. After the investigation of numerical chaotic behavior in the system, an adaptive feedback controller is designed to achieve the finite-time synchronization of two oscillators, based on the Lyapunov function. This controller could find application in many other fractional-order chaotic circuits. Applying synchronized fractionalorder systems in digital cryptography, a well secured key system is obtained. Numerical simulations are given to illustrate and verify the analytic results.

show abstract

Section: Introductionmentioning

confidence: 99%

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Consider two fractional order chaotic Duffing systems (see similar examples in [11,21,23]): The drive (master) system given by: …”

Section: Simulation Resultsmentioning

confidence: 99%

“…There exists many formulations for the fractional order derivative definition; the most popular are those of Grünwald-Letnikov (GL), RiemannLiouville (RL) and Caputo [22,23].…”

Section: Fractional Derivatives and Integralsmentioning

confidence: 99%

Chattering Elimination in Fuzzy Sliding Mode Control of Fractional Chaotic Systems Using a Fractional Adaptive Proportional Integral Controller

Khettab¹,

Bensafia²,

Ladaci³

2017

IJIES

View full text Add to dashboard Cite

Abstract:In this paper, a Fractional Adaptive Fuzzy Logic Control (FAFLC) strategy based on active fractional sliding mode (FSM) theory is considered to synchronize chaotic fractional-order systems. Takagi-Sugeno fuzzy systems are used to estimate the plant dynamics represented by unknown fractional order functions. One of the main contributions in this work is to combine an adaptive fractional order PI λ control law with the fractional-order adaptive sliding mode controller in order to eliminate the chattering action in the control signal. Based on Lyapunov theory, the stability analysis of the proposed control strategy is performed for an acceptable synchronization error level. Numerical simulations illustrate the efficiency of the proposed fractional fuzzy adaptive control scheme through the synchronization of two different fractional order chaotic Duffing systems. We show that the introduction of the additional fractional adaptive PI λ control action is able to eliminate the chattering phenomena in the control signal.

show abstract

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).…”

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.

View full text Add to dashboard Cite

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)

show abstract

Adaptive control and synchronization of a fractional-order chaotic system

Cited by 40 publications

References 25 publications

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

Chattering Elimination in Fuzzy Sliding Mode Control of Fractional Chaotic Systems Using a Fractional Adaptive Proportional Integral Controller

Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems

Contact Info

Product

Resources

About