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.     

一种分数阶混沌系统同步的自适应滑模控制器设计

针对分数阶混沌系统的同步问题, 基于滑模控制理论和自适应控制理论, 设计了一个具有较强鲁棒性的分数阶积分滑模面, 并提出了一种自适应滑模控制器在不消除非线性项的情况下实现一类三维分数阶混沌系统同步的方法. 利用所设计的自适应滑膜控制器实现了分数阶Chen系统、分数阶Liu系统以及分数阶Arneodo系统的混沌同步. 数值模拟仿真结果验证了所设计的控制器的有效性和可行性.     

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.     

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     

Chaotic synchronization for a class of fractional-order chaotic systems

In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-order systems, is simple and theoretically rigorous.     

Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance

Based on fractional-order Lyapunov stability theory, this paper provides a novel method to achieve robust modified projective synchronization of two uncertain fractional-order chaotic systems with external disturbance. Simulation of the fractional-order Lorenz chaotic system and fractional-order Chen＇s chaotic system with both parameters uncertainty and external disturbance show the applicability and the efficiency of the proposed scheme.     

Function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems

This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional (3D) integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.     

基于区间系统理论的分数阶混沌系统同步

通过设计一个非线性反馈控制器,实现了分数阶混沌系统的同步.与其他的分数阶混沌系统同步方法相比,提出的控制器设计方法保留了部分误差系统中的非线性项,而没有完全抵消同步误差系统的非线性项,有效改善了误差系统的控制性能.同时,应用区间分数阶线性时不变系统稳定性原理和线性矩阵不等式技术,得到了一个新的分数阶混沌系统同步的充分条件,进而获得的控制器保证了混沌系统同步.仿真结果验证了提出方法的有效性. 关键词： 区间分数阶时不变系统 分数阶混沌系统 混沌同步     

基于滑模控制实现分数阶混沌系统的投影同步

针对分数阶混沌系统的投影同步问题,提出了一种基于主动滑模原理的控制器.基于分数阶线性系统的稳定性理论,分析了该方法的稳定性.分别以同结构分数阶Liu-Liu系统的投影同步和异结构分数阶Chen-Liu系统的投影同步为例进行了数值仿真,仿真结果验证了主动滑模控制方法在分数阶混沌系统投影同步中的有效性. 关键词： 分数阶混沌系统 滑模控制 投影同步     

Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)

Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.     

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.     

A new kind of nonlinear phenomenon in coupled fractional-order chaotic systems: coexistence of anti-phase and complete synchronization

In this paper,we have found a kind of interesting nonlinear phenomenon-hybrid synchronization in linearly coupled fractional-order chaotic systems.This new synchronization mechanism,i.e.,part of state variables are anti-phase synchronized and part completely synchronized,can be achieved using a single linear controller with only one drive variable.Based on the stability theory of the fractional-order system,we investigated the possible existence of this new synchronization mechanism.Moreover,a helpful theorem,serving as a determinant for the gain of the controller,is also presented.Solutions of coupled systems are obtained numerically by an improved Adams-Bashforth-Moulton algorithm.To support our theoretical analysis,simulation results are given.     

A novel study on the impulsive synchronization of fractional-order chaotic systems

The stability of impulsive fractional-order systems is discussed.A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems.The synchronization criterion is suitable for the case of the order 0 q ≤ 1.It is more general than those of the known results.Simulation results are given to show the effectiveness of the proposed synchronization criterion.     

Adaptive synchronisation of fractional-order chaotic systems

A new stability theory of nonlinear dynamic systems is proposed, and a novel adaptive synchronisation method is presented for fractional-order chaotic and hyperchaotic systems based on the theory described in this paper. In comparison with previous methods, not only is the present control scheme simple but also it employs only one control strength, converges very fast, and it is also suitable for a large class of fractional-order chaotic and hyperchaotic systems. Moreover, this scheme is analytical and simple to implement in practice. Numerical and circuit simulations are used to validate and demonstrate the effectiveness of the method.     

Synchronization of chaotic fractional-order systems via active sliding mode controller

In this paper, we propose a controller based on active sliding mode theory to synchronize chaotic fractional-order systems in master-slave structure. Master and slave systems may be identical or different. Based on stability theorems in the fractional calculus, analysis of stability is performed for the proposed method. Finally, three numerical simulations (synchronizing fractional-order Lü-Lü systems, synchronizing fractional order Chen-Chen systems and synchronizing fractional-order Lü-Chen systems) are presented to show the effectiveness of the proposed controller. The simulations are implemented using two different numerical methods to solve the fractional differential equations.     

Synchronization between a novel class of fractional-order and integer-order chaotic systems via a sliding mode controller

<正>In order to figure out the dynamical behaviour of a fractional-order chaotic system and its relation to an integerorder chaotic system,in this paper we investigate the synchronization between a class of fractional-order chaotic systems and integer-order chaotic systems via sliding mode control method.Stability analysis is performed for the proposed method based on stability theorems in the fractional calculus.Moreover,three typical examples are carried out to show that the synchronization between fractional-order chaotic systems and integer-orders chaotic systems can be achieved. Our theoretical findings are supported by numerical simulation results.Finally,results from numerical computations and theoretical analysis are demonstrated to be a perfect bridge between fractional-order chaotic systems and integer-order chaotic systems.     

Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.     

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.     

基于单驱动变量分数阶混沌同步的参数调制数字通信及硬件实现

通过单驱动变量设计了三维分数阶混沌系统通用的自适应同步控制器.基于参数调制原理, 利用单驱动变量分数阶混沌系统的同步,提出了一种新的通用型数字通信方案,对电路进行了仿真,同时搭建了实际硬件电路,结果显示接收信息和发送信息符合完好,验证了本方案的有效性和可行性.