A Special Hybrid Projective Synchronization in Symmetric Chaotic System With Unknown Parameter

This paper investigates adaptive active control projective synchronization scheme. A general synchronization controller and parameter update laws are proposed to stabilize the error system for the identical structural chaotic systems. It is the first time that the active synchronization, the projective synchronization, and the adaptive synchronization are combined to achieve the synchronization of chaotic systems, which extend the control capability of achieving chaotic synchronization. By using a constant diagonal matrix, the active control is developed. Especially, when designing the controller, we just need to ensure that the diagonal elements of the diagonal matrix are less than or equal 0. So, the synchronization of chaotic systems can be realized more easily. Furthermore, by proposing an active controller, in combination with several different control schemes, we lower the complexity of the design process of the controller. More importantly, the larger the absolute value of product of the diagonal elements of diagonal matrix is, the smoother the curve of chaotic synchronization is and the shorter the time of chaotic synchronization is. In our paper, we take Lorenz system as an example to verify the effectiveness of the proposed synchronization scheme. Theoretical analysis and numerical simulations demonstrate the feasibility of this control method.

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A Novel Adaptive Active Control Projective Synchronization of Chaotic Systems

Quan

Wang

Sun

et al. 2018

Journal of Computational and Nonlinear Dynamics

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Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design

Dongmo

Ojo

Woafo

et al. 2018

Journal of Computational and Nonlinear Dynamics

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This paper introduces a new type of synchronization scheme, referred to as difference synchronization scheme, wherein the difference between the state variables of two master [slave] systems synchronizes with the state variable of a single slave [master] system. Using the Lyapunov stability theory and the active backstepping technique, controllers are derived to achieve the difference synchronization of three identical hyperchaotic Liu systems evolving from different initial conditions, as well as the difference synchronization of three nonidentical systems of different orders, comprising the 3D Lorenz chaotic system, 3D Chen chaotic system, and the 4D hyperchaotic Liu system. Numerical simulations are presented to demonstrate the validity and feasibility of the theoretical analysis. The development of difference synchronization scheme has increases the number of existing chaos synchronization scheme.

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State Synchronization for a Class of n-Dimensional Nonlinear Systems with Sector Input Nonlinearity via Adaptive Two-Stage Sliding Mode Control

Yang

Wang

et al. 2020

Mathematical Problems in Engineering

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This study addresses an adaptive two-stage sliding mode control (SMC) scheme for the state synchronization between two identical systems, which belong to a kind of n-dimensional chaotic system, by considering the appearance of lumped system uncertainties and external disturbances. The controlled system is assumed to be attached to sector nonlinearity for the control input. The proposed adaptive control scheme involves time-variable state-feedback gains, which are updated in accordance with the appropriate adapted rules without foreknown the certain information of nonlinear system dynamics, bounds of lumped system uncertainties and external disturbances, and sector input nonlinearity. The derivation of the control scheme is found based on the introduced sequence of two sliding functions. The stage 1 sliding function is defined by the states of the error dynamical system, where the asymptotical stability is inherent. Then, the stage 2 sliding function is formed by the stage 1 function, where the finite-time stabilization is guaranteed. The proposed adaptive control scheme can cope with the effect of sector nonlinearity for the control to meet the control goal. The sufficient conditions of the stability of the error dynamical system are proven mathematically by means of the Lyapunov theorem. Besides, the capacity of the present scheme is carried out by the numerical studies.

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A Special Hybrid Projective Synchronization in Symmetric Chaotic System With Unknown Parameter

Cited by 3 publications

References 18 publications

A Novel Adaptive Active Control Projective Synchronization of Chaotic Systems

A Novel Adaptive Active Control Projective Synchronization of Chaotic Systems

Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design

State Synchronization for a Class of n-Dimensional Nonlinear Systems with Sector Input Nonlinearity via Adaptive Two-Stage Sliding Mode Control

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