Adaptive Feedback Control for Synchronization of Chaotic Neural Systems with Parameter Mismatches

Ye, Qian; Jiang, Zhengxian; Chen, Tiane

doi:10.1155/2018/5431987

Cited by 17 publications

(15 citation statements)

References 23 publications

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“…Once the dynamics of the synchronization error (47) has been obtained, the following control law can be proposed:…”

Section: Ideal Case the Synchronization Error Can Be Defined Asmentioning

confidence: 99%

“…wherê,̂,̂,̂,̂, and̂are estimations of the unknown constant parameters , , , , , and , respectively; 1 , 2 , and 3 are positive constant gains selectable by the designer. By substituting (48) into (47), the closed-loop synchronization error dynamics is obtained aṡ1…”

Section: Ideal Case the Synchronization Error Can Be Defined Asmentioning

confidence: 99%

“…In technical literature, various strategies have been proposed for control of chaotic systems [41][42][43][44][45][46][47][48]. Three approaches have commonly been used when both the structure and the parameters of the system are known: linear feedback control [49][50][51][52][53], nonlinear control [54][55][56][57][58], and active control [59][60][61][62][63][64][65][66][67][68].…”

Section: Introductionmentioning

confidence: 99%

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Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control

Pérez-Cruz

2018

Complexity

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Standard adaptive control is the preferred approach for stabilization and synchronization of chaotic systems when the structure of such systems is a priori known but the parameters are unknown. However, in the presence of unmodeled dynamics and/or disturbance, this approach is not effective anymore due to the drift of the parameter estimations, which eventually causes the instability of the closed-loop system. In this paper, a robustifying term, which consists of a saturation function, is used to avoid this problem. The robustifying term is added to the adaptive control law. Consequently, the learning law is also modified. The boundedness of the states and the parameter estimations is rigorously and thoroughly proven by means of Lyapunov like analysis based on Barbalat’s lemma. On these new conditions, the convergence to zero cannot be achieved due to the presence of unmodeled dynamics and/or disturbance. However, it is still possible to guarantee the asymptotic convergence to a bounded zone around zero. The width of this zone can be adjusted by the designer. The performance of this robust approach is verified by numerical simulations. Although, for simplicity, this strategy is only applied to the stabilization and synchronization of Zhang system, the procedure can easily be generalized to a broad class of chaotic systems.

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“…Once the dynamics of the synchronization error (47) has been obtained, the following control law can be proposed:…”

Section: Ideal Case the Synchronization Error Can Be Defined Asmentioning

confidence: 99%

Section: Ideal Case the Synchronization Error Can Be Defined Asmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control

Pérez-Cruz

2018

Complexity

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“…A system is called as the chaotic system, provided that it exhibits chaos phenomenon. Due to its powerful potential applications in secure communications, biological systems, information processing, etc., the control of chaotic system has attracted extensive attention of scholars in recent 20 years, and many e cient approaches have been presented for controlling chaos, such as OGY control [1], impulsive control [2], fuzzy control [3,4], sliding mode control [5,6], adaptive control [7,8], composite learning control [9,10], and so on. Nowadays, many papers about controlling chaotic systems have been published.…”

Section: Introductionmentioning

confidence: 99%

A Novel Fast Convergence Control Scheme for a Class of 3D Chaotic Systems with Uncertain Parameters and External Disturbances

Luo

et al. 2020

Complexity

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This paper studies the control of a class of 3D chaotic systems with uncertain parameters and external disturbances. A new method which is referred as the analytical solution approach is firstly proposed for constructing Lyapunov function. Then, for suppressing the trajectories of the 3D chaotic system to its equilibrium point 00,0,0, a novel fast convergence controller containing parameter λ which determines the convergence rate of the system is presented. By using the designed Lyapunov function, the stability of the closed-loop system is proved via the Lyapunov stability theorem. Computer simulations are employed to a new chaotic system to illustrate the effectiveness of the theoretical results.

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“…The problem of the unidirectional synchronization of chaotic systems consists of finding an appropriate control law such that when this is applied to a system with coupled inputs called "slave" or "response," such system follows the dynamics of an autonomous chaotic system called "master" or "drive" [1][2][3][4][5][6][7][8][9][10][11]. This proper control action is necessary because, without it, two identical autonomous chaotic systems could never be synchronized due to their high sensitivity to initial conditions [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control

et al. 2019

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In this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master-slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. If the gain matrix and the matrices of Riccati equation are selected in such a way that a unique positive definite solution is obtained for this equation, then, with respect to previous works, a stronger result can be guaranteed here: the exponential convergence to zero of the synchronization error. Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. On this new condition, the synchronization error does not converge to zero anymore. However, it is still possible to guarantee the exponential convergence to a bounded zone. Numerical simulation confirms the satisfactory performance of the suggested approach.

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Adaptive Feedback Control for Synchronization of Chaotic Neural Systems with Parameter Mismatches

Cited by 17 publications

References 23 publications

Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control

Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control

A Novel Fast Convergence Control Scheme for a Class of 3D Chaotic Systems with Uncertain Parameters and External Disturbances

Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control

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