基于Lyapunov方程的分数阶混沌系统同步

对阶次小于1的分数阶系统提出了基于Lyapunov方程的系统稳定性判定理论. 将该理论应用于分数阶混沌系统的同步,实现了未知参数的分数阶Lorenz混沌系统的自适应同步. 仿真结果证实了该理论的正确性. 关键词： 分数阶混沌系统 同步 Lyapunov方程 自适应     

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.     

带有未知非对称控制增益的不确定分数阶混沌系统自适应模糊同步控制

针对带有非对称控制增益的不确定分数阶混沌系统的同步问题设计了模糊自适应控制器. 模糊逻辑系统用来逼近未知的非线性函数, 非对称的控制增益矩阵被分解为一个未知的正定矩阵、一个对角线上元素为+1或-1的已知对角矩阵和 一个未知的上三角矩阵的乘积. 基于分数阶Lyapunov稳定性理论构造了模糊控制器以及分数阶的参数自适应律, 在保证所有变量有界的情况下实现驱动系统和响应系统的同步. 在分数阶系统稳定性分析中给出了一种平方Lyapunov函数的使用方法, 根据此方法很多针对整数阶系统的控制方法可以推广到分数阶系统中. 最后数值仿真结果验证了所提控制方法的可行性.     

分数阶统一混沌系统的自适应同步

提出了分数阶统一混沌系统的自适应同步方法, 给出了自适应同步控制器和参数自适应率. 设计的单一控制器简单且只含有一个驱动变量. 所用同步方法适用于一类分数阶混沌系统的同步, 且具有较强的抗噪声能力, 具有较高的实用价值. 数值模拟结果表明了该方法的有效性. 关键词： 分数阶 统一混沌系统 自适应同步     

基于自适应主动及滑模控制的分数阶超混沌系统异结构反同步

以超混沌Chen系统和超混沌Lorenz系统为例,研究了慢时变参数超混沌系统的反同步问题.首先利用主动控制的思想,消去超混沌系统中的非线性部分,然后基于Lyapunov稳定性理论,合理地选取参数自适应控制律,很好的解决了时变参数的参数摄动问题,从而实现了两个超混沌系统的反同步.在此基础之上,又进一步研究了分数阶超混沌系统,使用滑模控制方法对其进行控制,理论上分析了该方法的可行性.数值模拟实验进一步验证了所提出方法的有效性. 关键词： 超混沌 分数阶 自适应 滑模     

自适应同步参数未知的异结构分数阶超混沌系统

基于分数阶系统稳定理论,实现了分数阶超混沌CYQY系统与参数未知的分数阶超混沌Lorenz系统间的异结构自适应同步.不仅设计了控制器,还设计了参数自适应规则并保留了非线性项.数值仿真证实了自适应控制器的有效性. 关键词： 分数阶 超混沌 同步 自适应     

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     

分数阶系统的一种稳定性判定定理及在分数阶统一混沌系统同步中的应用

根据Lyapunov稳定定理及其逆定理和分数阶系统稳定定理,提出了如果整数阶系统稳定,其对应的阶次小于1的分数阶形式的系统也稳定的分数阶系统稳定的判定定理,并给出了详细的证明过程.并将该理论运用于分数阶混沌系统的同步,实现了未知参数分数阶统一混沌系统的自适应同步,仿真结果证实了该理论的正确性. 关键词： 分数阶系统 混沌 Lyapunov稳定定理 Lyapunov稳定逆定理     

分数阶超混沌Chen系统和分数阶超混沌 Rössler系统的异结构同步

分数阶系统具有更大的密钥空间, 然而异结构的分数阶系统在保密通信领域更具有普遍性, 因此, 研究异结构的分数阶同步问题具有重要的意义. 本文讨论了分数阶超混沌Chen系统和分数阶超混沌Rössler系统的异结构同步问题, 基于分数阶系统稳定性理论, 应用主动控制同步法和自适应控制同步法来设计各自不同的控制器, 使得响应系统和驱动系统同步. 数值仿真表明了本文所研究方法的可行性和有效性.     

分数阶超混沌Chen系统和分数阶超混沌Rssler系统的异结构同步

分数阶系统具有更大的密钥空间,然而异结构的分数阶系统在保密通信领域更具有普遍性,因此,研究异结构的分数阶同步问题具有重要的意义.本文讨论了分数阶超混沌Chen系统和分数阶超混沌Rossler系统的异结构同步问题,基于分数阶系统稳定性理论,应用主动控制同步法和自适应控制同步法来设计各自不同的控制器,使得响应系统和驱动系统同步.数值仿真表明了本文所研究方法的可行性和有效性.     

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.     

不确定分数阶时滞混沌系统自适应神经网络同步控制

针对带有完全未知的非线性不确定项和外界扰动的异结构分数阶时滞混沌系统的同步问题,基于Lyapunov稳定性理论,设计了自适应径向基函数(radial basis function,RBF)神经网络控制器以及整数阶的参数自适应律.该控制器结合了RBF神经网络和自适应控制技术,RBF神经网络用来逼近未知非线性函数,自适应律用于调整控制器中相应的参数.构造平方Lyapunov函数进行稳定性分析,基于Barbalat引理证明了同步误差渐近趋于零.数值仿真结果表明了该控制器的有效性.     

Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems

In this paper, the adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems with unknown Lipschitz constant is investigated. Firstly, based on the adaptive control theory and the impulsive differential equations theory, the impulsive controller, the adaptive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, the new sufficient criterion is derived to guarantee the asymptotical stability of synchronization error system by the Lyapunov stability theory and the generalized Barbalat's lemma. In addition, numerical simulations demonstrate the effectiveness and feasibility of the proposed adaptive impulsive control method.     

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.     

Fuzzy adaptive synchronization of uncertain chaotic systems

This Letter presents an adaptive approach for synchronization of Takagi–Sugeno (T–S) fuzzy chaotic systems. Since the parameters of chaotic system are assumed unknown, the adaptive law is derived to estimate the unknown parameters and its stability is guaranteed by Lyapunov stability theory. The control law to be designed consists of two parts: one part that can stabilize the synchronization error dynamics and the other part that estimates the unknown parameters. Numerical examples are given to demonstrate the validity of the proposed adaptive synchronization approach.     

一种异结构分数阶混沌系统投影同步的新方法

基于Lyapunov稳定性理论和分数阶系统稳定理论以 及分数阶非线性系统性质,提出了一种用来判定分数阶混沌系统是 否稳定的新的判定定理,并把该理论运用于对分数阶混沌系统的控制与 同步,同时给出了数学证明过程,严格保证了该方法的正确性与一般适用性. 运用所提出的稳定性定理,实现了异结构分数阶混沌系统的投影同步. 对分数阶Lorenz混沌系统与分数阶Liu混沌系统实现了投影同步; 针对四维超混沌分数阶系统,也实现了异结构投影同步. 该稳定性定理避 免了求解分数阶平衡点以及Lyapunov指数的问题,从而可以方便地选 择出控制律,并且所得的控制器结构简单、适用范围广. 数值仿真的结果取得了预期的效果,进一步验证了这一稳定性定理的 正确性及普遍适用性.     

Designing synchronization schemes for fractional-order chaotic system via a single state fractional-order controller

In this paper the synchronization of fractional-order chaotic systems is studied and a new single state fractional-order chaotic controller for chaos synchronization is presented based on the Lyapunov stability theory. The proposed synchronized method can apply to an arbitrary three-dimensional fractional chaotic system whether the system is incommensurate or commensurate. This approach is universal, simple and theoretically rigorous. Numerical simulations of several fractional-order chaotic systems demonstrate the universality and the effectiveness of the proposed method.     

The adaptive synchronization of fractional-order Liu chaotic system with unknown parameters

In this paper, the chaos control and the synchronization of two fractional-order Liu chaotic systems with unknown parameters are studied. According to the Lyapunov stabilization theory and the adaptive control theorem, the adaptive control rule is obtained for the described error dynamic stabilization. Using the adaptive rule and a proper Lyapunov candidate function, the unknown coefficients of the system are estimated and the stabilization of the synchronizer system is demonstrated. Finally, the numerical simulation illustrates the efficiency of the proposed method in synchronizing two chaotic systems.     

Combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and disturbances

In this paper, the problem of combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and external interferences is studied. Firstly, the definition of combination projection synchronization of fractional-order complex dynamic networks is given, and the synchronization problem of the drive-response systems is transformed into the stability problem of the error system. In addition, time-varying delays and disturbances are taken into consideration to make the network synchronization more practical and universal. Then, based on Lyapunov stability theory and fractional inequality theory, the adaptive controller is formulated to make the drive and response systems synchronization by the scaling factors. The controller is easier to realize because there is no time-delay term in the controller. At last, the corresponding simulation examples demonstrate the effectiveness of the proposed scheme.