Fuzzy Adaptive Synchronization of Uncertain Fractional-Order Chaotic Systems

Boulkroune, Abdesselem; Bouzeriba, Amel; Bouden, Toufik; Azar, Ahmad Taher

doi:10.1007/978-3-319-30340-6_28

Cited by 63 publications

(17 citation statements)

References 47 publications

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“…A fuzzy logic system consists of four parts: the knowledge base, the fuzzifier, the fuzzy inference engine working on the fuzzy rules, and the defuzzifier [34][35][36][37][38][39][40]48]. Usually, a fuzzy logic system is modeled bŷ(…”

Section: Description Of a Fuzzy Systemmentioning

confidence: 99%

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Adaptive Fuzzy Synchronization of Fractional-Order Chaotic Neural Networks with Backlash-Like Hysteresis

Liu

2018

Advances in Mathematical Physics

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An adaptive fuzzy synchronization controller is designed for a class of fractional-order neural networks (FONNs) subject to backlash-like hysteresis input. Fuzzy logic systems are used to approximate the system uncertainties as well as the unknown terms of the backlash-like hysteresis. An adaptive fuzzy controller, which can guarantee the synchronization errors tend to an arbitrary small region, is given. The stability of the closed-loop system is rigorously analyzed based on fractional Lyapunov stability criterion. Fractional adaptation laws are established to update the fuzzy parameters. Finally, some simulation examples are provided to indicate the effectiveness and the robust of the proposed control method.

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Section: Description Of a Fuzzy Systemmentioning

confidence: 99%

“…Up to now, fuzzy control methods have been studied extensively [34][35][36][37][38][39][40][41][42]. Specially, this approach has been particularly used to synchronize or control integer-order neural networks (IONNs) [43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Fuzzy Synchronization of Fractional-Order Chaotic Neural Networks with Backlash-Like Hysteresis

Liu

2018

Advances in Mathematical Physics

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“…In the past two decades, synchronization of chaotic systems (CSs) has received more and more attention, and a lot of interesting works have been done, which have potential application values in secret communications, signal processing, and complex systems [1][2][3][4][5][6][7][8][9]. Recently, control and synchronization of fractional-order chaotic systems (FOCSs), which can be seen as a generalization of the integer-order CSs, have been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, control and synchronization of fractional-order chaotic systems (FOCSs), which can be seen as a generalization of the integer-order CSs, have been studied extensively. A lot of controllers have been implemented such as active control [10], feedback control [11], sliding mode control [12,13], adaptive control, [14,15], and adaptive fuzzy control [8,9,16].…”

Section: Introductionmentioning

confidence: 99%

Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems

Wang

2018

Advances in Mathematical Physics

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Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. A novel fractional-order sliding surface, which is composed of a synchronization error and its fractional-order integral, is introduced. The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. Finally, two numerical examples are given to show the feasibility of the proposed methods.

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“…Closed-loop control also includes methods such as backstepping control Rasappan and Vaidyanathan, 2012;Vaidyanathan et al, 2014, active control (Sundarapandian and Karthikeyan, 2012;Karthikeyan and Sundarapandian, 2014;Sarasu and Sundarapandian, 2011;Vaidyanathan and Rajagopal, 2011), adaptive control Vaidyanathan and Volos, 2015;Vaidyanathan et al, 2015e;Vaidyanathan and Pakiriswamy, 2015;Vaidyanathan and Azar, 2016a, 2016b, 2016c, 2016d, sliding mode control (Cao et al, 2016;Boujelben et al, 2016;Vaidyanathan and Sampath, 2012;Sundarapandian and Sivaperumal, 2011;Vaidyanathan, 2015u) and intelligent control (Boulkroune et al, 2016a(Boulkroune et al, , 2016bSadeghpour et al, 2012;Wang et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

A novel 4-D hyperchaotic system with two quadratic nonlinearities and its adaptive synchronisation

Vaidyanathan

Azar

Boulkroune

2018

IJAAC

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This work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. A qualitative analysis of the properties of the novel 4-D hyperchaotic system is presented. A special feature of our novel hyperchaotic system is that it has three equilibrium points of which two are unstable and one is locally asymptotically stable. The Lyapunov exponents of the novel hyperchaotic system are obtained as L1 = 1.5146, L2 = 0.2527, L3 = 0 and L4 = −12.7626. The Kaplan-Yorke dimension of the novel hyperchaotic system is derived as DKY = 3.1385. Next, this work describes the design of an adaptive controller for the global hyperchaos synchronisation of identical novel hyperchaotic systems with unknown parameters. MATLAB simulations are shown to describe all the main results derived in this work.

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Fuzzy Adaptive Synchronization of Uncertain Fractional-Order Chaotic Systems

Cited by 63 publications

References 47 publications

Adaptive Fuzzy Synchronization of Fractional-Order Chaotic Neural Networks with Backlash-Like Hysteresis

Adaptive Fuzzy Synchronization of Fractional-Order Chaotic Neural Networks with Backlash-Like Hysteresis

Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems

A novel 4-D hyperchaotic system with two quadratic nonlinearities and its adaptive synchronisation

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