Finite-time sliding mode synchronization of chaotic systems

A new finite-time sliding mode control approach is presented for synchronizing two different topological structure chaotic systems. With the help of the Lyapunov method, the convergence property of the proposed control strategy is discussed in a rigorous manner. Furthermore, it is mathematically proved that our control strategy has a faster convergence speed than the conventional finite-time sliding mode control scheme. In addition, the proposed control strategy can ensure the finite-time synchronization between the master and the slave chaotic systems under internal uncertainties and external disturbances. Simulation results are provided to show the speediness and robustness of the proposed scheme. It is worth noticing that the proposed control scheme is applicable for secure communications.     

冠状动脉系统高阶滑模自适应混沌同步设计

针对冠状动脉系统混沌同步问题, 系统模型受到有界但未知的不确定干扰条件下, 利用几何齐次性理论和积分滑模面设计高阶滑模自适应控制器, 使响应系统在有限时间内跟踪驱动系统, 该方法无需提前预知扰动边界. 采用Lyapunov理论对闭环系统进行分析并证明该控制器保证该系统能够在有限时间内镇定, 从仿真实验结果可以看出所设计的控制器在不确定干扰的情况下系统具有良好鲁棒性和未知参数的自适应性, 为能够有效治疗心肌梗死等冠状动脉疾病提供了一定的理论依据.     

Hybrid synchronization of hyperchaotic CAI systems via sliding mode control

In this paper, we investigate the hybrid chaos synchronization of identical hyper-chaotic CAI systems by sliding mode control. In hybrid chaos synchronization of master and slave systems, the odd states of two systems are completely synchronized, while their even states are anti-synchronized. The stability results derived in this paper for hybrid chaos synchronization of identical hyper-chaotic CAI systems are established using Lyapunov stability. Since the Lyapunov exponents are not required for these calculations, the sliding mode control is very effective and convenient to achieve hybrid chaos synchronization of the identical hyper-chaotic CAI systems. Numerical simulations are shown to validate and demonstrate the effectiveness of the synchronization schemes derived in this paper.     

Solitary wave solutions for some nonlinear time-fractional partial differential equations

In this paper, we have studied the hybrid projective synchronisation for incommensurate, integer and commensurate fractional-order financial systems with unknown disturbance. To tackle the problem of unknown bounded disturbance, fractional-order disturbance observer is designed to approximate the unknown disturbance. Further, we have introduced simple sliding mode surface and designed adaptive sliding mode controllers incorporating with the designed fractional-order disturbance observer to achieve a bounded hybrid projective synchronisation between two identical fractional-order financial model with different initial conditions. It is shown that the slave system with disturbance can be synchronised with the projection of the master system generated through state transformation. Simulation results are presented to ensure the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. Also, synchronisation error for commensurate, integer and incommensurate fractional-order financial systems is studied in numerical simulation.     

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.     

Chaos control and reduced-order generalized synchronization for the Chen——Liao system

This paper deals with the problem of chaos control and synchronization of the Chen--Liao system. From rigorous mathematic justification, the chaotic trajectories of the Chen--Liao system are led to a type of points whose four-dimensional coordinates have a particular functional relation among them. Meanwhile, a new synchronization manner, reduced-order generalized synchronization (RGS), is proposed which has the characteristic of having a functional relation between the slave and the partial master systems. It is shown that this new synchronization phenomenon can be realized by a novel technique. Numerical simulations have verified the effectiveness of the proposed scheme.     

Multi-switching dual compound synchronization of chaotic systems

A novel multi-switching dual compound synchronization scheme is proposed for chaotic systems which has not been investigated so far. The goal is to design appropriate controllers by using Lyapunov stability theory and nonlinear control to establish the asymptotically stable synchronized state for six drive and two response systems. Multi-switching dual compound synchronization can be considered as an extension of multi-switching dual combination synchronization. An example is presented to elaborate the proposed scheme where Lorenz, Chen, Lu systems are considered as master systems and T system is considered as slave system. The results obtained by theoretical and graphical analysis are in excellent agreement.     

Hybrid projective synchronization of chaotic fractional order systems with different dimensions

The hybrid projective synchronization of different dimensional fractional order chaotic systems is investigated in this paper. It is shown that the slave system can be synchronized with the projection of the master system generated through state transformation. Based on the stability theorem of linear fractional order systems, a suitable controller for achieving the synchronization is given. The hybrid projective synchronization between the fractional order chaotic system and hyperchaotic system is successfully achieved in both reduced order and increased order. The corresponding numerical results verify the effectiveness of the proposed method.     

Chaos synchronization based on intermittent state observer

This paper describes the method of synchronizing slave to the master trajectory using an intermittent state observer by constructing a synchronizer which drives the response system globally tracing the driving system asymptotically. It has been shown from the theory of synchronization error-analysis that a satisfactory result of chaos synchronization is expected under an appropriate intermittent period and state observer. Compared with continuous control method, the proposed intermittent method can target the desired orbit more efficiently. The application of the method is demonstrated on the hyperchaotic R?ssler systems. Numerical simulations show that the length of the synchronization interval τ_s is of crucial importance for our scheme, and the method is robust with respect to parameter mismatch.     

基于单向注入垂直腔面发射激光器系统的密钥分发

随机源对于信息理论安全的密钥分发至关重要,本文提出了一种基于单向注入垂直腔面发射激光器系统的密钥分发方案.首先基于单向注入的方式产生无时延特征的激光混沌信号,并通过单向注入驱动两个从激光器产生带宽增强的混沌同步信号.然后经过采样、量化以及异或等后处理,生成密钥流.数值仿真结果表明,在单阈值情况下,合法用户之间的误比特率低至1%左右,合法用户与窃听者之间的误比特率都高于10%;在双阈值情况下,误比特率可以低至10^-6.最后,对生成的密钥流进行了NIST随机性测试.该方案有效地增强了密钥分发的安全性.     

Experimental robust synchronization of hyperchaotic circuits

Even if complete synchronization between two chaotic circuits can be reached only when the systems are identical, in this paper we address the robustness of synchronization in the presence of parameter mismatches between the coupled circuits in the case of hyperchaotic behavior. In particular, a master–slave scheme based on negative feedback [T. Kapitaniak, Synchronization of chaos using continuous control, Phys. Rev. E 50 (1994) 1642–1644] is considered and the strategy to design the slave system as an observer of the master is given. With the proposed approach, based on the concept of the Master Stability Function, the two circuits are coupled through a unique scalar signal. Experimental results obtained from two hyperchaotic circuits will be presented in order to show that synchronization occurs widely in the range of electronic component tolerances.     

Adaptive synchronization of Chua＇s system with uncertain inputs

The synchronization of Chua's system, whose inputs include an unknown constant parameter, is studied in this paper. A constructive method is applied to designing an adaptive controller, in which only one variable information of the master system is needed. With the action of control signals, the parameter of the slave system will approach the corresponding unknown parameter in the master system. At the same time, the synchronization errors will also converge to zero asymptotically. Numerical simulations show that the proposed theoretical approach is very effective.     

Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

We investigate the projective synchronization of different chaotic systems with nonlinearity inputs.Based on the adaptive technique,sliding mode control method and pole assignment technique,a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor.     

Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

We investigate the projective synchronization of different chaotic systems with nonlinearity inputs. Based on the adaptive technique, sliding mode control method and pole assignment technique, a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor.     

基于滑模控制的分数阶混沌系统的自适应同步

基于滑模控制理论和自适应控制理论,研究了分数阶混沌系统的同步问题.设计了新的分数阶积分滑模面,并提出了用单一自适应控制器实现一类三维分数阶混沌系统同步的方法.数值模拟证实了所提方法的有效性. 关键词： 滑模控制 分数阶混沌系统 单一控制器 自适应同步     

基于分数阶滑模面控制的分数阶超混沌系统的投影同步

本文通过设计一个新型的含分数阶滑模面的滑模控制器,应用主动控制原理和滑模控制原理,实现了一个新分数阶超混沌系统和分数阶超混沌Chen系统的投影同步.应用Lyapunov理论,分数阶系统稳定理论和分数阶非线性系统性质定理对该控制器的存在性和稳定性分别进行了分析,并得到了异结构分数阶超混沌系统达到投影同步的稳定性判据.数值仿真采用分数阶超混沌Chen 系统和一个新分数阶超混沌系统的投影同步,仿真结果验证了方法的有效性. 关键词： 分数阶滑模面滑模控制器 稳定性分析 分数阶超混沌系统 投影同步     

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.     

基于不确定性变时滞分数阶超混沌系统的滑模自适应鲁棒的同步控制

针对一类含有不确定参数的时变时滞系统的同步控制问题,提出了一种滑模自适应鲁棒控制方法.基于Lyapunov稳定性理论和滑模自适应控制方法,设计出滑模自适应鲁棒控制器和参数自适应率.所设计的单一控制器适用于一类分数阶超混沌系统的同步性控制问题,它不仅具有较强的抗噪声能力而且对于时变时滞系统也具有良好的控制能力,因此该控制器具有较好的实用价值.此外,通过在系统的输入量中引入一个补偿量,用以消除系统中所存在的不确定性和外界扰动的影响,从而实现不确定性分数阶超混沌系统的同步,并且将系统的同步误差控制在任意小范围内.最后,对带有外界噪声扰动、系统参数不确定的时变时滞Chen分数阶超混沌系统进行了数值仿真,经过短暂的时间,响应系统与驱动系统同步,进而验证了所提出的控制方法的有效性.     

基于反演自适应动态滑模的FitzHugh-Nagumo神经元混沌同步控制

本文采用反演自适应动态滑模控制实现耦合FitzHugh-Nagumo (FHN) 神经元混沌同步. 该方法将自适应技术与反演控制方法相结合, 通过设计新型切换函数, 采用动态滑模控制律, 实现了带有不确定参数的耦合FHN神经元混沌放电同步. 研究表明该方法可以有效地削弱系统的抖振, 从而避免破坏神经元的本质特性, 且响应速度快. 仿真结果证明了该控制方法的有效性. 关键词： 自适应 动态滑模控制 FitzHugh-Nagumo神经元 混沌同步     

A Novel Adaptive Observer-Based Control Scheme for Synchronization and Suppression of a Class of Uncertain Chaotic Systems

A novel adaptive observer-based control scheme is presented for synchronization and suppression of a class of uncertain chaotic system. First, an adaptive observer based on an orthogonal neural network is designed. Subsequently, the sliding mode controllers via the proposed adaptive observer are proposed for synchronization and suppression of the uncertain chaotic systems. Theoretical analysis and numerical simulation show the effectiveness of the proposed scheme.