一类分数阶混沌系统的自适应同步

针对一类分数阶混沌系统的同步问题,基于分数阶系统的类Lyapunov稳定性理论,设计了一种新的自适应同步控制器以及控制增益系数自适应律.与现有结果相比,该方法具有控制器结构简单、控制代价小以及通用性强等特点,可适用于大部分典型的分数阶混沌系统.最后,数值仿真结果验证了所提方法运用于分数阶混沌系统同步研究的有效性.     

Global adaptive synchronization of chaotic systems with uncertain parameters

We propose a novel adaptive synchronization method for a class of nonlinear chaotic systems with uncertain parameters.Using the chaos control method,we derive a synchronizer,which can make the states of the driven system globally track the states of the drive system asymptotically.The advantage of our method is that our problem sctting is more general than those that already exist,and the synchronizer is simply constructed by an analytic formula,without knowledge in advance of the unknown bounds of the uncertain parameters.A computer simulation example is given to validate the proposed approach.     

Adaptive impulsive synchronization of uncertain chaotic systems

The Letter develops an adaptive impulsive scheme that includes a sole restriction criterion to achieve synchronization of chaotic nonlinear systems with unknown parameters. The system is assumed to satisfy the local Lipschitz condition while a Lipschitz constant and the uncertain system parameters are estimated by augmented adaptation equations. Adaptation of all parameters is proven to converge exponentially. The significance of the related control parameters and their margins in the criterion is also discussed in detail. The Lorenz system has been simulated to illustrate the theoretical analysis.     

不同结构混沌系统的自适应同步和反同步

针对不同结构混沌系统的同步与反同步问题进行了研究.在系统参数已知时,采用主动控制法实现混沌系统的同步与反同步,并将主动控制器的设计方法进行了推广.在参数未知时,基于Lyapunov稳定性理论和自适应控制方法,给出了自适应控制器和参数自适应律,实现了参数均未知且结构不同的驱动系统和响应系统的同步与反同步.在控制器的设计过程中,将驱动系统和响应系统进行互换,讨论了互换前后的控制器和自适应律之间的关系.数值仿真结果说明了所提出设计方法的有效性. 关键词： 混沌同步 反同步 主动控制法 自适应控制法     

Adaptive synchronization of Rossler and Chen chaotic systems

A novel adaptive synchronization method is proposed for two identical Rossler and Chen systems with uncertain parameters. Based on Lyapunov stability theory, we derive an adaptive controller without the knowledge of the system parameters, which can make the states of two identical Rossler and Chen systems globally asymptotically synchronized. Especially, when some unknown uncertain parameters are positive, we can make the controller more simple and, besides, the controller is independent of those positive uncertain parameters. All results are proved using a well-known Lyapunov stability theorem. Numerical simulations are given to validate the proposed synchronization approach.     

一类参数不确定混沌系统的自适应同步

基于Lyapunov稳定性原理,对一类参数不确定混沌系统,提出一种自适应同步控制方法.给出了自适应同步控制器和参数自适应律的解析表达式,对于具体的误差系统,控制器结构还可以进一步简化.该方法较为简单,适用范围广.以新混沌和超混沌Chen系统为例,数值模拟证明了该方法的有效性和可行性. 关键词： 参数不确定混沌系统 自适应同步 新混沌系统 超混沌Chen系统     

Robust synchronization of uncertain chaotic systems

This paper investigates robust unified (lag, anticipated, and complete) synchronization of two coupled chaotic systems. By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and the theory of robust stability, several criteria on robust synchronization are established. Extensive numerical simulations are also used to confirm the results.     

不确定自催化反应扩散时空混沌系统的延时同步

设计了一种延迟同步控制器实现了时空混沌系统之间的同步控制.基于Lyapunov稳定性定理,确定了延迟同步控制器的结构以及系统状态变量之间的误差方程.以自催化反应扩散时空混沌系统为例,仿真模拟验证了该控制器的有效性.进一步设计了参量辨识器,对不确定自催化反应扩散时空混沌系统中的参量进行了有效辨识.通过研究有界噪声影响下系统的同步效果,表明该同步方法具有较好的抗干扰能力. 关键词： 时空混沌 延时同步 参量辨识 有界噪声     

多涡卷混沌系统的广义同步控制

基于反步自适应方法,提出了一种在初值不同以及驱动系统参数未知的情况下,保持驱动和响应两多涡卷混沌系统同步的控制律设计方法.该方法所设计的控制律能够同时适用于两混沌系统的完全同步、反同步和一类非线性广义同步,具有较高的实用价值.仿真结果表明了所设计控制律的有效性. 关键词： 多涡卷混沌 广义同步 反步 自适应     

On multi switching compound synchronization of non identical chaotic systems

Multi switching compound synchronization (MSCOS) between four non identical chaotic systems is investigated. Chen system is considered as scaling drive system. Lorenz and Lü systems are taken as base drive systems. The compound of the multi drive system is then synchronized with Rössler response system using multi switching synchronization scheme. In MSCOS, the state variables of three drive systems synchronize with different state variables of response system, simultaneously. For suitable choice of scaling factors, switched modified function projective synchronization is obtained as a special case of MSCOS among chaotic systems. To achieve the desired synchronization among four non identical chaotic systems, sufficient condition is obtained using a nonlinear controller and Lyapunov stability theory, and corresponding theoretical proofs are given. The effectiveness of the proposed controllers is verified by numerical simulations using MATLAB.     

Adaptive generalized functional synchronization of chaotic systems with unknown parameters

A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R6ssler chaotic system and the four-dimensional Chen＇s hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed.     

Controlling projective synchronization in coupled chaotic systems

In this paper, a new method for controlling projective synchronization in coupled chaotic systems is presented. The control method is based on a partially linear decomposition and negative feedback of state errors. Firstly, the synchronizability of the proposed projective synchronization control method is proved mathematically. Then, three different representative examples are discussed to verify the correctness and effectiveness of the proposed control method.     

Robust pre-specified time synchronization of chaotic systems by employing time-varying switching surfaces in the sliding mode control scheme

In the conventional chaos synchronization methods, the time at which two chaotic systems are synchronized, is usually unknown and depends on initial conditions. In this work based on Lyapunov stability theory a sliding mode controller with time-varying switching surfaces is proposed to achieve chaos synchronization at a pre-specified time for the first time. The proposed controller is able to synchronize chaotic systems precisely at any time when we want. Moreover, by choosing the time-varying switching surfaces in a way that the reaching phase is eliminated, the synchronization becomes robust to uncertainties and exogenous disturbances. Simulation results are presented to show the effectiveness of the proposed method of stabilizing and synchronizing chaotic systems with complete robustness to uncertainty and disturbances exactly at a pre-specified time.     

连续时间混沌系统的自适应Ｈ∞ 同步方法

提出了一种连续时间混沌系统的自适应H∞同步方法.当响应系统没有受噪声干扰影 响时，所设计的自适应H∞同步控制器能够使响应系统与驱动系统全局同步.当响应 系统受噪声干扰影响时，自适应H∞同步控制器能够使噪声干扰对同步误差的影响小于期望的水平.最后，以蔡氏电路混沌系统为例来说明所提方法的有效性. 关键词： 混沌 混沌同步 自适应控制 H∞控制 自适应H∞同步     

Adaptive synchronization of uncertain Liu system via nonlinear input

This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with total parameters unknown. This method is simple and can be easily designed. What is more, it improves the existing conclusions in Ref [12]. Simulation results prove that the controller is effective and feasible in the end.     

Complete synchronization of uncertain chaotic dynamical network via a simple adaptive control

In this paper, based on the invaxiance principle of differential equations, we propose a simple adaptive control method to synchronize the network with coupling of the general form. Comparing with other control approaches, this scheme only depends on each node＇s state output. So we need not to know the concrete network structure and the solutions of the isolate nodes of the network in advance. In order to demonstrate the effectiveness of the method, a special example is provided and numerical simulations are performed. The numerical results show that our control scheme is very effective and robust against the weak noise.     

Complete synchronization of uncertain chaotic dynamical network via a simple adaptive control

In this paper, based on the invariance principle of differential equations, we propose a simple adaptive control method to synchronize the network with coupling of the general form. Comparing with other control approaches, this scheme only depends on each node's state output. So we need not to know the concrete network structure and the solutions of the isolate nodes of the network in advance. In order to demonstrate the effectiveness of the method, a special example is provided and numerical simulations are performed. The numerical results show that our control scheme is very effective and robust against the weak noise.     

延迟混沌系统投影同步及状态切换的电路实验

利用有源低通滤波器设计了延迟混沌电路,利用低通滤波器的相频特性完成对混沌信号的延时,实现了单向耦合延迟混沌电路的投影同步及不同状态之间的切换.     

强耦合混沌系统中的近似同步

以单向驱动耦合Lorenz振子一维链为研究对象，研究振子间的混沌同步行为. 数值计算结果表明，对于变量y驱动x的耦合方式，在合适的耦合强度下，会出现第一个振子和第二个振子不同步，而与次近邻非直接连接的振子(如第三个振子)近似同步. 进一步研究表明，出现这一现象的原因是在大耦合强度下，对于这种驱动方式，第一个振子和第二个振子间出现驱动单变量近似同步；虽然它们之间未出现所有变量的完全同步，但是驱动信号事实上已经传递下去了. 关键词： Lorenz振子 混沌同步 近似同步     

Adaptive synchronization of chaotic systems with less measurement and actuation

We investigate the synchronization problem between identical chaotic systems only when necessary measurement(output) and actuation(input) are needed to be implemented by the adaptive controllers. A sufficient condition is derived based on the Lyapunov stability theory and Schur complementary lemma. Moreover, the theoretic result is applied to the Rikitake system and the hyperchaotic Liu system to show its effectiveness and correctness. Numerical simulations are presented to verify the results.