Synchronization of the bidirectionally coupled unified chaotic system via sum of squares method (original) (raw)
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Synchronization of generalised linearly bidirectionally coupled unified chaotic system
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Several important properties of chaos synchronization of bidirectionally coupled systems remain still unexplored. This paper investigates identical synchronization scheme for generalised linearly bidirectionally coupled unified chaotic system. The Lyapunov stability theory is used to substantiate the results. The study of linearly bidirectionally coupled unified chaotic systems are done first and conditions on coupling parameters for synchronization are derived. Finally, numerical simulation results are presented to show the feasibility and effectiveness of the approach.
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2013
This paper proposes the synchronization control method for two different unified chaotic systems with unknown mismatched parameters using sum of squares method. Previously, feedback-linearizing and stabilization terms were used in the controller for the synchronization problem. However, they used just a constant matrix as a stabilization control gain, whose performance is shown to be valid only for a linear model. Thus, we propose the novel control method for the synchronization of the two different unified chaotic systems with unknown mismatched parameters via sum of squares method. We design the stabilization control input which is of the polynomial form by sum of squares method and also the adaptive law for the estimation of the unknown mismatched parameter between the master and slave systems. Since we can use the polynomial control input which is dependent on the system states as the stabilization controller, the proposed method can have better performance than the previous methods. Numerical simulations for both uni-directional and bi-directional chaotic systems show the validity and advantage of the proposed method.
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The unified chaotic system incorporates the behaviors of the Lorenz, the Chen and the Lü chaotic systems. This paper deals with the synchronization of two identical unified chaotic systems where the slave system is assumed to have a single input. A sliding mode controller is proposed to synchronize the two systems. The asymptotic convergence to zero of the errors between the states of the master and the slave systems is shown. Simulations results are presented to illustrate the proposed controller; they indicate that the designed controller is able to synchronize the unified chaotic systems. Also, simulation results show that the proposed control scheme is robust to random bounded disturbances acting on the master system. Moreover, the proposed scheme is applied to the secure communications field, where simulation results indicate that the proposed scheme is effective.
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ASURVEY AND COMPARISON ON SYNCHRONIZATION METHODS OF CHAOTIC SYSTEMS
In this paper, several methods forsynchronization of chaotic systems are explained and compared. The idea is based on drive-response systems synchronization. The methods include: active Control, recursive control, adaptive control, and partial linearizationmethod which are implemented and applied to a Lorenz chaotic system. The partial linearization method is used to synchronize a subset of states of the system to synchronize other states as well. Active control and rebound control methods are used when the system parameters are known while adaptive control method is used when some of the parameters of the system are unknown. Inthesemethods,synchronization is based on Lyapunov stability theory. Three methods, namely, adaptive, active and recursive and are implemented on a T system successfully. A newmatrix method has been presented for synchronization based on the theory of Lyapanovkrakfskytheory and linear matrix inequality (LMI).This method has been implemented to a Rösslersystem with delay. Comparingto classical methods used to synchronize chaotic system the matrix method seems the best because of easy design of input, suitable for synchronization of chaotic systems with delay, simple calculations, no need to find aLyapunov function for stability.
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International Journal of Dynamics and Control, 2015
In this paper, two different methods for two(bi)directional generalized synchronization of chaotic systems are proposed. The coupling based scheme provides a strategy to design suitable coupling functions to achieve synchronization. The controller based scheme relies on designing a suitable control input for achieving generalized synchronization and works irrespective of the nature of coupling between the systems. The two proposed schemes are applied to identical as well as non identical Sprott N and Sprott Q chaotic systems to illustrate their effectiveness. Numerical simulations are performed for empirical evidence of the theoretical work.
Global chaos synchronization of new chaotic systems via nonlinear control
Chaos, Solitons & Fractals, 2005
Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e T e. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach.
Engineering, Technology & Applied Science Research
The problem of chaos synchronization is to design a coupling between two chaotic systems (master-slave/drive-response systems configuration) such that the chaotic time evaluation becomes ideal and the output of the slave (response) system asymptotically follows the output of the master (drive) system. This paper has addressed the chaos synchronization problem of two chaotic systems using the Nonlinear Control Techniques, based on Lyapunov stability theory. It has been shown that the proposed schemes have outstanding transient performances and that analytically as well as graphically, synchronization is asymptotically globally stable. Suitable feedback controllers are designed to stabilize the closed-loop system at the origin. All simulation results are carried out to corroborate the effectiveness of the proposed methodologies by using Mathematica 9.