Synchronization of uncertain chaotic systems with parameters perturbation via active control

Zhang, Hao; Ma, Xikui

doi:10.1016/j.chaos.2003.09.014

Cited by 84 publications

(29 citation statements)

References 11 publications

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“…3.2, to synchronize the Lorenz-Chen systems, someone need to change the sliding surfaces (s i ) as well as switching gains (k i ) because the same cannot be synchronized at the same sliding surface with same switching gains(Figs. 9,10,11,12,13,14,15), whereas in Sect. 3.6, Liu-Lorenz systems synchronize quickly for the same values as in Sect.…”

mentioning

confidence: 92%

“…So, synchronization of chaotic systems with uncertainties and external disturbances is effectively significant in applications. In this direction, researchers have proposed a number of techniques for synchronization of uncertain identical and non-identical chaotic systems [9][10][11][12][13][14][15][16][17][18]. All abovementioned techniques were based on with fully (or partially) known parameters for the systems.…”

mentioning

confidence: 99%

“…Time series of x 1 and y 1 with EU and ED Time series of x 2 and y 2 with EU and ED Time series of x 3 and y 3 with EU and ED Time series of e 1 , e 2 and e 3 with EU and ED Time series of x 1 and y 1 with EU and ED 1 (t) u 2 (t) u 3 (t) Time series of x 3 and y 3 with EU and ED Time series ofV (t) Time series of e 1 , e 2 and e 3 with EU and EDwhere u i (t) for i = 1, 2, 3 are the controllers govern as per the rule (2.9) and the Liu-Lorenz systems (when perturbed by EU and ED) are simulated for the initial values of master and slave systems:[5, −3, 10] and[10,2,4] respectively, the vector of switching gains (k i ) : 10 and sliding surface parameters (λ i ) :[15,15,10].…”

mentioning

confidence: 99%

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The improved results with Mathematica and effects of external uncertainty and disturbances on synchronization using a robust adaptive sliding mode controller: a comparative study

Shahzad

2014

Nonlinear Dyn

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In this computational article, the improved results when different chaotic systems are synchronized using robust adaptive sliding mode controller (RASMC) has been presented in which the simulation is based on Mathematica as well as the effects of external uncertainties (EU) and external disturbances (ED) have been studied in the synchronization of two different chaotic systems. For the same pairs (master and slave systems) of considered chaotic systems (Lorenz, Chen and Liu) and implemented technique (RASMC), a comparative study has been done between the results obtained using Mathematica and MATLAB, as well as the effects of EU and ED on the convergence of synchronization have been studied.

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confidence: 92%

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confidence: 99%

mentioning

confidence: 99%

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The improved results with Mathematica and effects of external uncertainty and disturbances on synchronization using a robust adaptive sliding mode controller: a comparative study

Shahzad

2014

Nonlinear Dyn

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“…A static output feedback controller was designed to guarantee H ∞ synchronization between the master and slave systems. In [27][28][29], a linear state feedback control via the linear matrix inequality (LMI) approach was proposed for robust synchronization of uncertain chaotic systems with different parameters perturbation on both master system and slave system. A verified sufficient condition formulated in the LMI form was derived to ensure system stability.…”

Section: Introductionmentioning

confidence: 99%

Intelligent quadratic optimal synchronization of uncertain chaotic systems via LMI approach

Chen

2010

Nonlinear Dyn

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This paper proposes an intelligent quadratic optimal control scheme via linear matrix inequality (LMI) approach for the synchronization of uncertain chaotic systems with both external disturbances and parametric perturbations. First, a four-layered neural fuzzy network (NFN) identifier is constructed to estimate system nonlinear dynamics. Based on the NFN identifier, an intelligent quadratic optimal controller is developed with robust hybrid control scheme, in which H ∞ optimal control and variable structure control (VSC) are embedded to attenuate the effects of external disturbances and parametric perturbations. The adaptive tuning laws of network parameters are derived in the sense of the Lyapunov synthesis approach to ensure network convergence, and the sufficient criterion for existence of the controller is formulated in the linear matrix inequality (LMI) form to guarantee the quadratic optimal synchronization performance. Finally, a numerical simulation example is illustrated by the chaotic Chua's circuit system to demonstrate the effectiveness of our scheme.

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“…Since then, synchronization of chaotic systems have been widely studied. Many methods have been designed to synchronize chaotic systems, such as active control [11], adaptive control [12] and so on. However, all aforementioned works amid of chaotic synchronization based on Lyapunov theory and set the error of driven system and response system to be zero when the time goes to infinity.…”

Section: Introductionmentioning

confidence: 99%

A Practical Synchronization Approach for Memristive Hyperchaotic System

Meng¹,

Zhang²,

Han³

et al. 2018

Proceedings of the 2018 International Conference on Mathematics, Modelling, Simulation and Algorithms (MMSA 2018)

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Abstract-Chaotic synchronization has great potential applications in engineering, physics and mathematics. Memristive hyperchaotic system synchronization is a hot spot for synchronization study. A practical synchronization approach is used in this paper. Compared with previous synchronization methods, this approach does not need the error of driven system and response system to be zero when the time goes to infinity. Detailed mathematical proof of this synchronization method is given to verify the electiveness. Finaly, a memristive hyperchaotic system is used to test the synchronization approach and the simulation results indicate that this method is elective.

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Synchronization of uncertain chaotic systems with parameters perturbation via active control

Cited by 84 publications

References 11 publications

The improved results with Mathematica and effects of external uncertainty and disturbances on synchronization using a robust adaptive sliding mode controller: a comparative study

The improved results with Mathematica and effects of external uncertainty and disturbances on synchronization using a robust adaptive sliding mode controller: a comparative study

Intelligent quadratic optimal synchronization of uncertain chaotic systems via LMI approach

A Practical Synchronization Approach for Memristive Hyperchaotic System

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