Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

Xin, Baogui; Wu, Zhi Fen

doi:10.3390/e17052677

Cited by 10 publications

(7 citation statements)

References 28 publications

(36 reference statements)

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“…Xu [21] showed that the scaling factor of PS in coupled partially linear systems is unpredictable and can be arbitrarily maneuvered by introducing a feedback control to master systems. The PS between two chaotic discrete dynamical systems was achieved by Xin and Wu [22] via linear state error feedback control. Wen and Xu [23] and Yan and Li [24] extended the projective synchronization feature to general nonlinear systems, including non-partially linear chaotic systems, by applying controllers to response systems, which is called generalized projective synchronization (GPS) and was studied later [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters

Zhen

2023

Applied Sciences

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This study proposes a new approach to realize generalized function projective synchronization (GFPS) between two different chaotic systems with uncertain parameters. The GFPS condition is derived by converting the differential equations describing the synchronization error systems into a series of Volterra integral equations on the basis of the Laplace transform method and convolution theorem, which are solved by applying the successive approximation method in the theory of integral equations. Compared with the results obtained by constructing Lyapunov functions or calculating the conditional Lyapunov exponents, the uncertain parameters and the scaling function factors considered in this paper have fewer restrictions, and the parameter update laws designed for the estimation of the uncertain parameters are simpler and easier to realize physically.

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Section: Introductionmentioning

confidence: 99%

Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters

Zhen

2023

Applied Sciences

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“…We can formulate the 0-1 test algorithm [16][17][18][19][20][21] as follows. Suppose φ(n) is a discrete set of measurement data sampled at times n = 1, 2, 3, · · · , N, where N is the total amount of the data.…”

Section: -1 Test Algorithm For Chaosmentioning

confidence: 99%

Neimark–Sacker Bifurcation Analysis and 0–1 Chaos Test of an Interactions Model between Industrial Production and Environmental Quality in a Closed Area

Xin

2015

Sustainability

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A discrete-time model is presented to describe the complex interaction between industrial production and environmental quality in a closed area. Its Neimark-Sacker bifurcation and chaos are discussed based on Wen's explicit Neimark-Sacker bifurcation criterion, Kuznetsov's normal form method and center manifold theory and Gottwald and Melbourne's 0-1 test algorithm. Numerical simulations are employed to validate the main results of this work.

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“…At present, there are an increasing number of control theories, and parts of them even have been applied in practice for many years such as PID control [8,9], adaptive control [10][11][12][13], and feedback control [14][15][16] and so on. On the contrary, many remarkable state-of-the-art control methods, which enjoy a variety of advantages compared to traditional control methods, are being developed.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Predictive Control of a Hydropower System Model

Zhang

Chen

2015

Entropy

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A six-dimensional nonlinear hydropower system controlled by a nonlinear predictive control method is presented in this paper. In terms of the nonlinear predictive control method; the performance index with terminal penalty function is selected. A simple method to find an appropriate terminal penalty function is introduced and its effectiveness is proved. The input-to-state-stability of the controlled system is proved by using the Lyapunov function. Subsequently a six-dimensional model of the hydropower system is presented in the paper. Different with other hydropower system models; the above model includes the hydro-turbine system; the penstock system; the generator system; and the hydraulic servo system accurately describing the operational process of a hydropower plant. Furthermore, the numerical experiments show that the six-dimensional nonlinear hydropower system controlled by the method is stable. In addition, the numerical experiment also illustrates that the nonlinear predictive control method enjoys great advantages over a traditional control method in nonlinear systems. Finally, a strategy to combine the nonlinear predictive control method with other methods is proposed to further facilitate the application of the nonlinear predictive control method into practice.

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Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

Cited by 10 publications

References 28 publications

Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters

Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters

Neimark–Sacker Bifurcation Analysis and 0–1 Chaos Test of an Interactions Model between Industrial Production and Environmental Quality in a Closed Area

Nonlinear Predictive Control of a Hydropower System Model

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