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.     

Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller

This Letter investigates chaos synchronization of chaotic and hyperchaotic systems. Based on finite-time stability theory, a simple adaptive control method for realizing chaos synchronization in a finite time is proposed. In comparison with previous methods, the present method is not only simple, but could also be easily utilized in application. Numerical simulations are given to illustrate the effectiveness and validity of the proposed approach.     

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.     

Adaptive lag synchronization and parameters adaptive lag identification of chaotic systems

This Letter investigates the problem of adaptive lag synchronization and parameters adaptive lag identification of chaotic systems. In comparison with those of existing parameters identification schemes, the unknown parameters are identified by adaptive lag laws, and the delay time is also identified in this Letter. Numerical simulations are also given to show the effectiveness of the proposed method.     

Hyperchaos of four state autonomous system with three positive Lyapunov exponents

This Letter gives the results of numerical simulations of Quantum Cellular Neural Network (Quantum-CNN) autonomous system with four state variables. Three positive Lyapunov exponents confirm hyperchaotic nature of its dynamics.     

广义Hénon混沌系统的自适应双模控制与同步

提出一种广义Hénon映射的自适应双模控制与同步方法.广义Hénon映射的混沌吸引子比Hénon映射的混沌吸引子更复杂,控制与同步困难,对于保密通信来说具有更高的安全性.该方法采用自适应双模控制,实现了广义Hénon映射的追踪控制与同步,提高了受控系统抑制参数摄动和随机扰动的能力,改善系统的鲁棒性.仿真结果验证了该方法的有效性.     

Adaptive control and synchronization for chaotic systems with parametric uncertainties

An adaptive control scheme using only part of the system states for the stabilization of one chaotic system and the synchronization of two chaotic systems is presented. The system parameters are allowed to have a large range of time varying uncertainties around their fixed unknown nominal values both in the stabilization and the synchronization control problems. Simulation results also illustrate the effectiveness of the proposed control scheme.     

Adaptive synchronization of a class of continuous chaotic systems with uncertain parameters

This Letter investigates the problem of synchronization between two different chaotic systems. A generic adaptive synchronization scheme is proposed for a class of chaotic systems with uncertain parameters. Based on the Lyapunov stability theorem, an adaptive controller and the corresponding parameters update laws are designed to synchronize two chaotic systems. Numerical simulations are also given to show the effectiveness of the proposed method.     

参数不确定的分数阶混沌系统广义错位延时投影同步

为进一步增强通信系统中保密通信的安全性,结合广义错位投影同步和延时投影同步,提出了广义错位延时投影同步.以分数阶Chen系统和Lü系统为例,针对两系统参数都不确定,基于分数阶稳定性理论与自适应控制方法,设计了非线性控制器和参数自适应律,实现了广义错位延时同步,并辨识出驱动系统和响应系统中所有不确定参数.理论分析和数值仿真验证了该方法的可行性与有效性.     

Adaptive generalized projective synchronization of two different chaotic systems with unknown parameters

This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov stability theory, and employs a combination of feedback control and adaptive control. With this method one can achieve the generalized projective synchronization and realize the parameter identifications between almost all chaotic （hyperchaotic） systems with unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.     

Chaos synchronization of unified chaotic systems via LMI

This Letter focuses on the master-slave synchronization problem of the unified chaotic systems. Based on Lyapunov stability theory and linear matrix inequality (LMI) formulation, a simple linear feedback control law is obtained to make the state of two identical unified chaotic systems asymptotically synchronized. Simulation results have illustrated the effectiveness of the proposed chaos synchronization solution.     

利用白噪声实现混沌系统线性广义同步的研究

给定一个混沌驱动系统和同步函数，通过服从白噪声分布的单向耦合，构造出混沌响应系统，使之与驱动系统达到线性广义同步化.研究发现，利用满足一定条件的白噪声可以实现驱动-响应系统的线性广义同步.以Chua电路为例进行了数值仿真，其结果与理论计算相一致. 关键词： 混沌系统 广义同步 白噪声     

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.     

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.     

Generalized projective synchronization of a class of chaotic (hyperchaotic) systems with uncertain parameters

In this paper is investigated the generalized projective synchronization of a class of chaotic (or hyperchaotic) systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic (hyperchaotic) systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic Lü system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.     

An integral control for synchronization of a class of unknown non-autonomous chaotic systems

In this Letter, a high gain integral controller for synchronization of unknown non-autonomous chaotic systems is proposed. Perturbation theory is used to demonstrate that the synchronization error of the resulting feedback system converges to zero. Numerical simulations are presented to illustrate the effectiveness of the proposed method.     

LMI-based robust adaptive synchronization of FitzHugh-Nagumo neurons with unknown parameters under uncertain external electrical stimulation

This Letter addresses a nonlinear robust adaptive control that utilizes linear matrix inequalities for asymptotic synchronization of two coupled chaotic FitzHugh-Nagumo neurons under unknown parameters and uncertain stimulation current amplitudes and phase shifts. Synchronization of chaotic neurons using the proposed control method through numerical simulation is demonstrated.     

混沌系统的自适应多变量广义预测控制与同步

提出了一种应用带时变遗忘因子的自适应多变量广义预测控制算法(β-MGPC)，对Lorenz，Rossler，Chua电路等典型混沌系统进行控制，使之跟踪任意给定参考信号，数值仿真表明了该控制算法的良好效果.这种方法的优点在于无需知道混沌系统的精确模型，便可实现混沌系统的大范围的跟踪和同步控制. 关键词： 混沌控制 混沌同步 自适应预测控制 时变遗忘因子     

Hénon混沌系统的广义预测控制与同步快速算法

提出了一种带有终端滑模等式约束的Hénon混沌系统的广义预测控制快速算法.该方法将广义预测控制与离散滑模控制结合起来运用到Hénon混沌系统中，并采用柔化输入信号的方法，避免了广义预测控制算法中的高维矩阵求逆.占用内存小，计算速度快，并且具有较强的跟踪给定信号和抑制系统参数摄动和随机噪声的能力.仿真结果验证了该方法的有效性和快速性. 关键词： 广义预测控制 离散滑模控制 Hénon混沌系统 混沌同步