Adaptive feedback controller for projective synchronization

Hu, Manfeng; Xu, Zhi-Hong

doi:10.1016/j.nonrwa.2007.03.005

Cited by 91 publications

(33 citation statements)

References 30 publications

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“…A basic configuration for chaos synchronization is the master-slave pattern, where the slave chaotic system must track the master chaotic trajectory. A number of methods based on this configuration have been proposed [4][5][6][7][8][9][10][11][12][13][14], such as feedback approach [4,5,6], time-delay feedback approach [7,8,9], adaptive method [10,11], backstepping design technique [12,13], Impulse control method [14], sliding mode control method [15] and so on.…”

Section: Introductionmentioning

confidence: 99%

Chaos Synchronization of a Class of Chaotic Systems via Linear State Error Feedback Control

Du¹,

Wang²,

Han³

2016

Proceedings of the 2nd International Conference on Advances in Mechanical Engineering and Industrial Informatics (AMEII 2016)

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Abstract. This paper studies the synchronization problem of a class of chaotic systems. The mentioned synchronization scheme consists of identical master and slave chaotic systems. By analyzing structural characteristics of nonlinear vector field of the error system, a new approach is presented to synchronize the two chaotic systems. Based on linear error state feedback, an independent stable equation of some error state variables is separated. Synchronization conditions is derived which make globally synchronization between the master system and the slave system rapidly. The approach can be used to achieve synchronization of the Genesio chaotic system and Liu chaotic system. A class of simple linear feedback controller is designed and precise corresponding synchronization conditions is obtained. Numerical examples illustrate the validity of the presented approach in this paper.

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Section: Introductionmentioning

confidence: 99%

Chaos Synchronization of a Class of Chaotic Systems via Linear State Error Feedback Control

Du¹,

Wang²,

Han³

2016

Proceedings of the 2nd International Conference on Advances in Mechanical Engineering and Industrial Informatics (AMEII 2016)

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“…For it's potential applications in secure communication, chemical and biological systems, information science and many other fields, lots of researches on the synchronization of coupled chaotic dynamical systems have been done and many theoretical and experimental results have been obtained [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Such as feedback control methods [5][6][7], backstepping design technique [8], impulsive control method [9], fuzzy sliding mode control method [10], adaptive method [11,12] and other kind of synchronization [13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Synchronization Between Two Different Switched Chaotic Systems By Switching Control

Wang

2016

MATEC Web Conf.

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Abstract. This paper is concerned with the synchronization problem of two different switched chaotic systems, considering the general case that the master-slave switched chaotic systems have uncertainties. Two basic problems are considered: one is projective synchronization of switched chaotic systems under arbitrary switching; the other is projective synchronization of switched chaotic systems by design of switching when synchronization cannot achieved by using any subsystems alone. For the two problems, common Lyapunov function method and multiple Lyapunov function method are used respectively, an adaptive control scheme has been presented, some sufficient synchronization conditions are attainted, and the switching signal is designed . Finally, the numerical simulation is provide to show the effectiveness of our method.

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“…Such sufficient conditions depended on the second smallest eigenvalue of the Laplacian matrix in case that the graph was undirected. After this work, many control schemes such as adaptive control [9,10], pinning control [11,12], fuzzy control [13], impulsive control [14][15][16], and intermittent control [17][18][19] are widely applied to achieve synchronization of complex dynamical networks.…”

Section: Introductionmentioning

confidence: 99%

Synchronization for complex networks with Markov switching via matrix measure approach

Pan

Cao

2015

Applied Mathematical Modelling

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a b s t r a c tThis paper devotes to almost sure synchronization and almost sure quasi-synchronization of complex networks with Markov switching. Some sufficient conditions are derived in terms of the ergodic theory of continuous time Markov chain and the matrix measure approach, which can guarantee that the dynamical networks almost surely synchronize or quasi-synchronize to a given manifold. According to the property of Markov chain and the exponential distribution of switching time sequence, we also estimate the probability distribution of the quasi-synchronization error for a two-state Markov chain and then generalize them to a finite state space Markov chain. Meanwhile, some examples with numerical simulations are given to show that the Markov chain plays an important role in synchronization of networks.

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Adaptive feedback controller for projective synchronization

Cited by 91 publications

References 30 publications

Chaos Synchronization of a Class of Chaotic Systems via Linear State Error Feedback Control

Chaos Synchronization of a Class of Chaotic Systems via Linear State Error Feedback Control

Synchronization Between Two Different Switched Chaotic Systems By Switching Control

Synchronization for complex networks with Markov switching via matrix measure approach

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