Synchronization of chaotic systems with different orders

A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state variables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.     

Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems

We investigate the synchronization of a class of incommensurate fractional-order chaotic systems,and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory,the fractional order differential inequality,and the adaptive strategy.This synchronization approach is simple,universal,and theoretically rigorous.It enables the synchronization of0 fractional-order chaotic systems to be achieved in a systematic way.The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.     

Synchronization Scheme for Uncertain Chaotic Systems via RBF Neural Network

A sliding mode adaptive synchronization controller is presented with a neural network of radial basis function （RBF） for two chaotic systems. The uncertainty of the synchronization error system is approximated by the RBF neural network. The synchronization controller is given based on the output of the RBF neural network. The proposed controller can make the synchronization error convergent to zero in 5s and can overcome disruption of the uncertainty of the system and the exterior disturbance. Finally, an example is given to illustrate the effectiveness of the proposed synchronization control method.     

Exponential networked synchronization of master-slave chaotic systems with time-varying communication topologies

The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory, a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a time- varying communication topology connection. The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory. The derived novel criteria are in the form of linear matrix inequalities (LMIs), which are easy to examine and tremendously reduce the computation burden from the feedback matrices. This paper provides an alternative networked secure communication scheme which can be extended conveniently. An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method.     

A single adaptive controller with one variable for synchronization of fractional-order chaotic systems

In this paper we investigate the synchronization of a class of three-dimensional fractional-order chaotic systems.Based on the Lyapunov stability theory and adaptive control technique,a single adaptive-feedback controller is developed to synchronize a class of fractional-order chaotic systems.The presented controller which only contains a single driving variable is simple both in design and in implementation.Numerical simulation and circuit experimental results for fractional-order chaotic system are provided to illustrate the effectiveness of the proposed scheme.     

Synchronization of different chaotic systems via active radial basis functions sliding mode controller

This paper presents a new method to synchronize different chaotic systems with disturbances via an active radial basis function （RBF） sliding controller. This method incorporates the advantages of active control, neural network and sliding mode control. The main part of the controller is given based on the output of the RBF neural networks and the weights of these single layer networks are tuned on-line based on the sliding mode reaching law. Only several radial basis functions are required for this controller which takes the sliding mode variable as the only input. The proposed controller can make the synchronization error converge to zero quickly and can overcome external disturbances. Analysis of the stability for the controller is carried out based on the Lyapunov stability theorem. Finally, five examples are given to illustrate the robustness and effectiveness of the proposed synchronization control strategy.     

Backstepping synchronization of uncertain chaotic systems by a single driving variable

In this paper a parameter observer and a synchronization controller are designed to synchronize unknown chaotic systems with diverse structures. Based on stability theory the structures of the observer and the controller are presented. The unknown Coullet system and Rossler system are taken for examples to demonstrate that the method is effective and feasible. The artificial simulation results show that global synchronization between the unknown Coullet system and the Rossler system can be achieved by a single driving variable with co-operation of the observer and the controller, and all parameters of the Coullet system can be identified at the same time.     

Synchronization of hyperchaotic Chen systems: a class of the adaptive control approach

The synchronization of hyperchaotic Chen systems is considered. An adaptive synchronization approach and a cascade adaptive synchronization approach are presented to synchronize a drive system and a response system. By utilizing an adaptive controller based on the dynamic compensation mechanism, exact knowledge of the systems is not necessarily required, and the synchronous speed is controllable by tuning the controller parameters. Sufficient conditions for the asymptotic stability of the two synchronization schemes are derived. Numerical simulation results demonstrate that the adaptive synchronization scheme with four control inputs and the cascade adaptive synchronization scheme with only one control signal are effective and feasible in chaos synchronization of hyperchaotic systems.     

Fuzzy modeling and impulsive control of hyperchaotic Lü system

This paper presents a novel approach to hyperchaos control of hyperchaotic systems based on impulsive control and the Takagi--Sugeno (T--S) fuzzy model. In this study, the hyperchaotic Lü system is exactly represented by the T--S fuzzy model and an impulsive control framework is proposed for stabilizing the hyperchaotic Lü system, which is also suitable for classes of T--S fuzzy hyperchaotic systems, such as the hyperchaotic R?ssler, Chen, Chua systems and so on. Sufficient conditions for achieving stability in impulsive T--S fuzzy hyperchaotic systems are derived by using Lyapunov stability theory in the form of the linear matrix inequality, and are less conservative in comparison with existing results. Numerical simulations are given to demonstrate the effectiveness of the proposed method.     

A secure communication method for a high-power information signal based on chaotic masking

In this paper,we present a secure communication method for a high-power information signal based on chaotic masking.In the transmitter,an adaptive controller is adopted to pick up the change of the information signal ,and to inject the controller‘s error into the transmitting system.At the same time,the information is directly added to the chaotic signal in transmission to drive the receiving system.In the receiver,another adaptive controller is used to maintain chaotic synchronization of the transmitting and receiving systems and to recover the information signal.Since the synchronization error is independent from the information signal,the power of the information signal can be equivalent to that of the chaotic signal,and the frequency of the information signal can be set within the range of the principal frequencies of the chaotic signal,The results of theoretical analysis and numerical simulation show that the presented method not only enhances the degree of security of low-dimensional chaotic systems but also significantly improves the signal-to-noise ratio at the receiving end.     

Synchronisation of chaotic systems using a novel sampled-data fuzzy controller

This paper presents the synchronisation of chaotic systems using a sampled-data fuzzy controller and is meaningful for many physical real-life applications. Firstly, a Takagi--Sugeno (T--S) fuzzy model is employed to represent the chaotic systems that contain some nonlinear terms, then a type of fuzzy sampled-data controller is proposed and an error system formed by the response and drive chaotic system. Secondly, relaxed LMI-based synchronisation conditions are derived by using a new parameter-dependent Lyapunov--Krasovskii functional and relaxed stabilisation techniques for the underlying error system. The derived LMI-based conditions are used to aid the design of a sampled-data fuzzy controller to achieve the synchronisation of chaotic systems. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.     

基于自适应模糊控制的分数阶混沌系统同步

本文主要研究了带有未知外界扰动的分数阶混沌系统的同步问题.基于分数阶Lyapunov稳定性理论,构造了分数阶的参数自适应规则以及模糊自适应同步控制器.在稳定性分析中主要使用了平方Lyapunov函数.该控制方法可以实现两分数阶混沌系统的同步,使得同步误差渐近趋于0.最后,数值仿真结果验证了本文方法的有效性.     

一类多时滞混沌系统的主从容错同步

研究了一类多时滞混沌系统的主从容错同步问题.所设计的同步方法无论混沌系统中是否有故障发生,都可以使混沌主从同步误差系统全局渐近稳定并且满足给定的性能指标.容错同步方法的控制器包含两个部分:状态反馈控制器和故障补偿器.控制器的存在条件是时滞依赖的并可以通过线性矩阵不等式的方法进行求解.最后通过仿真验证了设计方法的有效性.     

含不确定性混沌系统的模糊自适应同步

研究了含不确定性混沌系统的同步问题.基于Takagi-Sugeno(T-S)模糊动态模型，给出了一个新的自适应模糊同步控制设计方法.该方法同时适用于相同结构混沌系统的同步以及异构混沌系统的同步.为说明问题，给出了Lorenz混沌系统和Rossler混沌系统的同步控制设计和仿真结果. 关键词： 混沌系统 模糊控制 同步     

基于模糊滑模的有限时间混沌同步实现

提出了混沌同步有限时间实现问题.应用全程滑模控制技术，选择指数型终端滑模趋近律来设计滑模控制器，以实现一类混沌系统的状态同步.该设计方案针对混沌系统的参数不确定性和外界扰动，引入模糊基函数网络，在线估计不确定性和外部扰动的界值.同时该方案消除了滑模控制的到达阶段，状态始终保持在滑模面上，并能在有限时间内趋近于原点.最后以Duffing系统为例研究验证同步策略的可行性和有效性.     

Adaptive fuzzy synchronization for a class of fractional-order neural networks

In this paper, synchronization for a class of uncertain fractional-order neural networks with external disturbances is discussed by means of adaptive fuzzy control. Fuzzy logic systems, whose inputs are chosen as synchronization errors,are employed to approximate the unknown nonlinear functions. Based on the fractional Lyapunov stability criterion, an adaptive fuzzy synchronization controller is designed, and the stability of the closed-loop system, the convergence of the synchronization error, as well as the boundedness of all signals involved can be guaranteed. To update the fuzzy parameters,fractional-order adaptations laws are proposed. Just like the stability analysis in integer-order systems, a quadratic Lyapunov function is used in this paper. Finally, simulation examples are given to show the effectiveness of the proposed method.     

基于模糊观测器的Chua混沌系统投影同步

研究了Chua混沌系统的广义投影同步问题.基于Takagi-Sugeno(T-S)模糊模型,设计了一种模糊观测器.利用Lyapunov稳定性理论证明了所提方案的可行性和全局稳定性.数值仿真试验进一步验证了该方案可以实现Chua混沌系统的投影同步.方法设计简单,且可以推广到其他的一些混沌系统. 关键词： T-S模糊模型 Chua混沌系统 观测器 投影同步     

Composite adaptive fuzzy control for synchronizing generalized Lorenz systems

This paper presents a methodology of asymptotically synchronizing two uncertain generalized Lorenz systems via a single continuous composite adaptive fuzzy controller (AFC). To facilitate controller design, the synchronization problem is transformed into the stabilization problem by feedback linearization. To achieve asymptotic tracking performance, a key property of the optimal fuzzy approximation error is exploited by the Mean Value Theorem. The composite AFC, which utilizes both tracking and modeling error feedbacks, is constructed by introducing a series-parallel identification model into an indirect AFC. It is proved that the closed-loop system achieves asymptotic stability under a sufficient gain condition. Furthermore, the proposed approach cannot only synchronize two different chaotic systems but also significantly reduce computational complexity and implemented cost. Simulation studies further demonstrate the effectiveness of the proposed approach.     

Adaptive fuzzy nonlinear inversion-based control for uncertain chaotic systems

<正>This paper presents a robust output feedback control method for uncertain chaotic systems,which comprises a nonlinear inversion-based controller with a fuzzy robust compensator.The proposed controller eliminates the unknown nonlinear function by using a fuzzy system,whose inputs are not the state variables but feedback error signals.The underlying stability analysis as well as parameter update law design are carried out by using the Lyapunov-based technique.The proposed method indicates that the nonlinear inversion-based control approach can also be applied to uncertain chaotic systems.Theoretical results are illustrated through two simulation examples.     

基于LMI的参数未知时变时滞混沌系统模糊自适应H_∞同步

考虑一类结构相同但驱动系统参数未知的两个时变时滞混沌系统同步问题,提出了基于T-S模糊模型的模糊自适应H∞同步方法.基于Lyapunov稳定性理论和线性矩阵不等式技术,给出了驱动系统参数未知时变时滞混沌系统同步的充分条件.仿真结果表明了所提方法的有效性.