Adaptive synchronization of different dimensional chaotic systems with unknown parameters

This paper addresses the adaptive synchronization and parameters identification problem of a class of high-dimensional autonomous uncertain chaotic systems. It is proved that the controller and update rule can make the states of the drive system and the response system with unknown system parameters asymptotically synchronized, and identify the response system's unknown parameters. Chen system, coupled dynamos system and Rössler hyperchaotic system are used as examples for detailed description. The results of numerical simulations show the effectiveness of the adaptive controller.

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Adaptive Synchronization of Fractional Hyper-Chaotic System with Unknown Parameters

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.850-851.868 ◽

2013 ◽

Vol 850-851 ◽

pp. 868-871 ◽

Cited By ~ 1

Author(s):

Li Xin Yang ◽

Wan Sheng He ◽

Jin Ping Jia ◽

Fan Di Zhang

Keyword(s):

Fractional Order ◽

Tracking Control ◽

Chaos Synchronization ◽

Chaotic Systems ◽

Adaptive Synchronization ◽

Uncertain Parameters ◽

Unknown Parameters ◽

Fractional Systems ◽

Control Approach ◽

The Stability

In this paper, chaos synchronization of the modified Sprott E system is investigated. Based on the stability theorem for fractional systems, tracking control approach is used for the fractional-order systems with uncertain parameters. Meanwhile, suitable adaptive synchronization controller and recognizing rules of the uncertain parameters are designed. Numerical simulation results show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order hyper-chaotic systems.

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ADAPTIVE ROBUST SYNCHRONIZATION FOR A CLASS OF DIFFERENT UNCERTAIN CHAOTIC SYSTEMS

International Journal of Modern Physics B ◽

10.1142/s0217979208048784 ◽

2008 ◽

Vol 22 (23) ◽

pp. 4069-4082 ◽

Cited By ~ 5

Author(s):

XINGYUAN WANG ◽

MINGJUN WANG

Keyword(s):

Chaotic Systems ◽

Adaptive Controller ◽

Adaptive Synchronization ◽

Unknown Parameters ◽

Robust Controller ◽

Synchronization Problem ◽

Robust Synchronization ◽

Response Systems ◽

Uncertain Chaotic Systems ◽

Predicted Values

This paper addresses the adaptive synchronization problem of a class of different uncertain chaotic systems. A general adaptive robust controller and parameters update rule are designed. It is proved theoretically that the controller and update rule can make the drive-response systems with different structures asymptotically synchronized, and change the unknown parameters to constants when noise exists. When the drive system is certain, the unknown parameters of the response system can be updated to the predicted values. The results of numerical simulations show the effectiveness of the adaptive controller.

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Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller

Abstract and Applied Analysis ◽

10.1155/2013/452549 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12

Author(s):

Zengyun Wang ◽

Lihong Huang ◽

Xuxin Yang ◽

Dingyang Lu

Keyword(s):

Chaotic Systems ◽

Sliding Mode ◽

Lyapunov Theory ◽

Adaptive Synchronization ◽

Sliding Mode Controller ◽

Unknown Parameters ◽

Adaptive Sliding Mode ◽

Adaptive Sliding Mode Controller ◽

Main Work ◽

Robust Adaptive

This paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. Secondly, we design an adaptive sliding mode controller to realize the asymptotical synchronization in mean squares. Thirdly, we design an adaptive sliding mode controller to realize the almost surely synchronization. Finally, the designed adaptive sliding mode controllers are used to achieve synchronization between two pairs of different stochastic chaos systems (Lorenz-Chen and Chen-Lu) in the presence of the uncertainties and unknown parameters. Numerical simulations are given to demonstrate the robustness and efficiency of the proposed robust adaptive sliding mode controller.

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