Synchronizing chaotic systems using control based on tridiagonal structure

Liu, Bin; Zhou, Yuefei; Jiang, Min; Zhang, Zengke

doi:10.1016/j.chaos.2007.06.099

Cited by 15 publications

(13 citation statements)

References 13 publications

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“…The control function u(t) is added into the slave system. System initial conditions are x(0) = [0, 0] T and y(0) = [1, 1] T for the master and slave systems, respectively, and the proposed control input signal, using (30), is described as (44) To design the equivalent part of control signal, the input variables of the fuzzy systemsf (y|θ f ) and [58] fuzzy system for u f s = FSMC(s,ṡ) are chosen as [s n ,ṡ n ], where s n = s/5 andṡ n =ṡ/50 are the normalized values of s andṡ, then we define seven type-2 Gaussian membership functions as shown in Fig. 4(a).…”

Section: Simulation Resultsmentioning

confidence: 99%

Synchronization of two different chaotic systems using novel adaptive interval type-2 fuzzy sliding mode control

et al. 2011

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In this paper, we use sliding mode control integrated with an interval type-2 fuzzy system for synchronization of two different chaotic systems in presence of system unmodeling and external disturbances. To reduce the chattering and improve the robustness of reaching phase of the Sliding Mode Control (SMC), an interval fuzzy type-2 logic controller is used. In addition, an adaptive interval type-2 fuzzy inference approximator is proposed (as equivalent control part of SMC) to approximate the unknown parts of the uncertain chaotic system. Using type-2 fuzzy systems makes more effective synchronization results in presence of system uncertainty and disturbances in comparison with type-1 fuzzy approximators. The stability analysis for the proposed control scheme is provided, and simulation results compare the performance of interval type-2 fuzzy and type-1 fuzzy con-M. Roopaei ( ) · trollers to verify the effectiveness of the proposed method.

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Section: Simulation Resultsmentioning

confidence: 99%

Synchronization of two different chaotic systems using novel adaptive interval type-2 fuzzy sliding mode control

et al. 2011

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“…In [35][36][37], the authors proposed a direct design method to achieve chaos synchronization. Two advantages of this method are to present an easy procedure for choosing proper controllers in chaos synchronization and construct simple controllers easily to implement.…”

Section: Synchronization Schemementioning

confidence: 99%

Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

et al. 2019

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This paper discusses the synchronization problem of N-coupled fractional-order chaotic systems with ring connection via bidirectional coupling. On the basis of the direct design method, we design the appropriate controllers to transform the fractional-order error dynamical system into a nonlinear system with antisymmetric structure. By choosing appropriate fractional-order Lyapunov functions and employing the fractional-order Lyapunov-based stability theory, several sufficient conditions are obtained to ensure the asymptotical stabilization of the fractional-order error system at the origin. The proposed method is universal, simple, and theoretically rigorous. Finally, some numerical examples are presented to illustrate the validity of theoretical results.

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“…And in [23] the authors also synchronized some chaotic systems based on the tridiagonal structure theory. The tridiagonal structure theorem as follows:…”

Section: Theory Of Tridiagonal Structure Matrix Stabilitymentioning

confidence: 99%

Controlling Chaos in Permanent Magnet Synchronous Motor Based on Tridiagonal Matrix Stability Theory

Tong¹,

Li²,

Wei³

2011

2011 3rd International Workshop on Intelligent Systems and Applications

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When system parameters falling into a certain area, the permanent magnet synchronous motor (PMSM) is experiencing chaotic behavior, which threatens the secure and stable operation of drive system. To control the undesirable chaos in PMSM, a new controller is proposed based on tridiagonal structure matrix stability theory. The proposed controller has some advantages: it is very simple and easy to be implemented; the control transition time is very short; it's robust against external interference. Simulation results are presented to show the effectiveness and robust of the controller.

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Synchronizing chaotic systems using control based on tridiagonal structure

Cited by 15 publications

References 13 publications

Synchronization of two different chaotic systems using novel adaptive interval type-2 fuzzy sliding mode control

Synchronization of two different chaotic systems using novel adaptive interval type-2 fuzzy sliding mode control

Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

Controlling Chaos in Permanent Magnet Synchronous Motor Based on Tridiagonal Matrix Stability Theory

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