Adaptive fuzzy synchronization of discrete-time chaotic systems

Vasegh, Nastaran; Majd, Vahid Johari

doi:10.1016/j.chaos.2005.08.123

Cited by 25 publications

(10 citation statements)

References 17 publications

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“…A unified approach to controlling chaos via LMIbased fuzzy control system design was suggested in [23] where the key idea is to use the well-known Takagi-Sugeno (T-S) fuzzy model to represent typical chaos models and then apply some effective fuzzy control techniques. Following the idea of representing chaotic systems via the T-S fuzzy model, some adaptive control methods have been proposed for stabilization or synchronization of discrete-time chaotic systems [24][25][26]. However, the modeling error and unknown disturbances are not considered in [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Directly adaptive fuzzy control of discrete-time chaotic systems by least squares algorithm with dead-zone

Jiang

2010

Nonlinear Dyn

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A new design scheme of directly adaptive fuzzy control for a class of discrete-time chaotic systems is proposed in this paper. The T-S fuzzy model is employed to represent the discrete-time chaotic systems. Then a fuzzy controller is designed and the unknown coefficients of the controller are identified by least squares algorithm with dead-zone. By Lyapunov method, all the signals involved in the closed-loop systems are shown to be bounded and the error between the system output and the reference output is proved to converge to a small neighborhood of zero. Simulation results demonstrate the effectiveness of the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Directly adaptive fuzzy control of discrete-time chaotic systems by least squares algorithm with dead-zone

Jiang

2010

Nonlinear Dyn

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“…(a) Chaotic attractors of systems (1) and (17) (b) Errors between systems (1) and (17) (c) Time evolutions of x and xs (1) and (17) with the second control law.…”

Section: The Second Control Law (Equation (18b))mentioning

confidence: 99%

“…Based on the second control law of Proposition 1, the linear controllers can be set into the following form: Figure 3a, the blue chaotic attractor of the master systems (1) is twice as large as the red one of the slave systems (17). Their synchronization errors 1 e , 2 e , 3 e between systems (1) and (17) .…”

Section: The Second Control Law (Equation (18b))mentioning

confidence: 99%

“…Li et al [16] proposed a backstepping control method to achieve adaptive function projective synchronization for a general class of the so-called strict-feedback chaotic discrete systems. Vasegh and Majd [17] presented a Takagi-Sugeno fuzzy model-based adaptive approach to synchronize two different chaotic discrete-time systems. Zhang et al [18] designed an impulsive controller to achieve impulsive lag synchronization for a class of chaotic discrete systems.…”

Section: Introductionmentioning

confidence: 99%

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Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

Xin

2015

Entropy

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A projective synchronization scheme for a kind of n-dimensional discrete dynamical system is proposed by means of a linear feedback control technique. The scheme consists of master and slave discrete dynamical systems coupled by linear state error variables. A kind of novel 3-D chaotic discrete system is constructed, to which the test for chaos is applied. By using the stability principles of an upper or lower triangular matrix, two controllers for achieving projective synchronization are designed and illustrated with the novel systems. Lastly some numerical simulations are employed to validate the effectiveness of the proposed projective synchronization scheme.

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“…Yau [11] presented a robust fuzzy sliding mode control scheme for the synchronization of two chaotic nonlinear gyros subject to uncertainties and external disturbances. Moreover, a growing body of researches [12][13][14][15][16][17] has emerged in order to address the synchronization of two chaotic nonlinear gyros.…”

Section: Introductionmentioning

confidence: 99%

Chaos Synchronization of Two Chaotic Nonlinear Gyros Using Backstepping Design

Loembe-Souamy

Jiang

Cheng

et al. 2015

Mathematical Problems in Engineering

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We investigate the chaos synchronization of two certain chaotic gyros using the backstepping approach. We design a simple controller and verify the stability of the error system by using proper Lyapunov functions. The designed control laws ensure stable controlled and synchronized states for two chaotic nonlinear gyros. Numerical simulations are implemented for illustration and verification of the effectiveness of the backstepping technique.

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Adaptive fuzzy synchronization of discrete-time chaotic systems

Cited by 25 publications

References 17 publications

Directly adaptive fuzzy control of discrete-time chaotic systems by least squares algorithm with dead-zone

Directly adaptive fuzzy control of discrete-time chaotic systems by least squares algorithm with dead-zone

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

Chaos Synchronization of Two Chaotic Nonlinear Gyros Using Backstepping Design

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