非线性耦合分数阶Chen混沌系统和网络的同步

利用非线性函数耦合混沌同步方法,讨论分数阶Chen混沌系统的同步问题,分析初始值和耦合系数的选择对于实现混沌同步的影响。并将该方法推广,实现规则网络的混沌同步。通过数值模拟实验,验证所提出方法的有效性。     

基于分数阶陈氏混沌系统的图像加密算法

由于分数阶混沌动力学系统比整数阶系统具有更复杂的动力学特性,且能为图像加密方案提供更多的自由度,基于分数阶陈氏混沌系统,提出了一种图像加密方法。在发送端,驱动系统产生混沌信号,利用混沌信号扰乱明文图像的像素位置,将扰乱后的图像掩盖在混沌信号中,得到传输的密文图像。在接收端,通过同步系统去掩盖,进行像素位置扰乱的逆操作,恢复明文图像。最后对提出的加密算法进行了安全性分析。实验结果表明,该加密算法安全性高,具有良好的研究价值和应用前景     

基于分数阶积分器的分数阶混沌系统状态观测器同步研究

提出了一种基于分数阶积分器的分数阶混沌系统状态观测器同步算法。通过引入一个新的变量,该变量是将驱动系统的输出信号与传输信道中干扰的和进行分数阶积分处理,然后再作为输入信号加到观测系统中,以便实现分数阶混沌系统的状态观测系统同步。然后利用Lyapunov稳定性理论和线性矩阵不等式证明了该方法的正确性。将该同步方法应用于分数阶Chen混沌系统,得出了同步误差曲线,仿真结果表明了该同步方法的有效性,最终实现了分数阶混沌系统的状态观测器同步。     

Synchronization of fractional-order uncertain chaotic systems with input nonlinearity

In this paper, sliding mode control has been designed for synchronization of fractional order uncertain chaotic systems with input nonlinearity. First, sliding mode control law has been taken from chaotic state error system which is asymptotically stable. Second, the shown sliding mode control ensures that fractional-order error system is asymptotically stable in the presence of uncertainty and nonlinear input. Simulation results using MATLAB software show that the designed controller is able to synchronize fractional-order chaotic systems in the presence of the mentioned factors.     

Intelligent fuzzy controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

In this research work, a novel fuzzy adaptive control is proposed to achieve a projective synchronization for a class of fractional-order chaotic systems with input nonlinearities (dead-zone together with sector nonlinearities). These master-slave systems under consideration are supposed to be with distinct models, different fractional-orders, unknown models, and dynamic external disturbances. The proposed control law consists of two main terms, namely: a fuzzy adaptive control term for appropriately approximating the uncertainties and a fractional-order variable-structure control term for robustly dealing with these inherent input nonlinearities. A Lyapunov approach is used to derive the updated laws and to prove the stability of the closed-loop control system. At last, a set of computer simulation results is carried out to illustrate and further validate the theoretical findings.     

分数阶混沌系统时域数值仿真及其可靠性分析

通过分析系统不动点的稳定性,得到分数阶微分系统存在混沌的解析条件。以分数阶统一混沌系统为例,通过时域数值仿真实验,发现时域近似产生的仿真误差会产生对分数阶微分系统是否存在混沌的错误判断,并且误差影响会随参数k的增大而变大。     

基于自适应神经网络的分数阶混沌系统滑模同步

针对一类异结构不确定分数阶混沌系统的同步问题,基于Lyapunov稳定性理论和分数阶系统稳定性理论,提出一种神经网络结合干扰观测器的主动反馈控制方法. 设计一种非线性干扰观测器对干扰进行观测,通过滑模控制对未观测出的部分干扰进行补偿,最终实现分数阶混沌系统的同步.与现有方法相比,采用的模型更符合工程应用实际,且不需要已知不确定项上界.数值仿真验证了所提出方法的有效性和正确性.     

Chaotic shuffled frog leaping algorithms for parameter identification of fractional-order chaotic systems

An accurate mathematical model has a vital role in controlling and synchronisation of chaotic dynamic systems. This paper proposes a shuffled frog leaping (SFL) algorithm and two chaotic versions of it to detect the unknown parameters and orders of chaotic models. The SFL by a grouping search strategy can provide a good exploration of search space. Also an independent local search for each group in this algorithm provides a proper exploitation ability. In the current research, to help the SFL to jump out of the likely local optima and to provide a better stochastic property to increase its convergence rate and resulting precision, the chaotic mapping is incorporated with the SFL. The superiority of the proposed algorithms is investigated on parameter identification of several typical fractional-order chaotic systems. Numerical simulation, comparisons with some typical existing algorithms and non-parametric analysis of obtained results show that the proposed methods have effective and robust performance. A considerably better performance of proposed algorithms based on average of objective functions demonstrates that the proposed idea can evolve robustness and consistence of SFL.     

不同阶分数阶混沌系统的同步与参数辨识

针对不确定分数阶混沌系统的同步和参数辨识问题,提出一种新的方法,即用不同阶分数阶系统来同步和参数辨识.利用主动控制和预控制量方法,基于分数阶混沌系统稳定性理论和自适应控制理论,设计控制器,实现不同阶分数阶混沌系统之间的同步和参数辨识.理论和仿真结果实现了不同阶Chen 系统间的同步和辨识,表明了该方法的有效性.     

分数阶混沌系统数值解析与电路仿真研究*

针对如何分析分数阶混沌系统的问题,基于改进的Adams-Bashforth-Moulton算法,研究了一个新三维分数阶混沌系统的数值解析方法,采用MATLAB软件平台,获得了该系统在不同分数阶时生成的混沌吸引子。基于频域近似法,采用RC串并联电路设计了分数阶单元电路,由一个模拟电路实现了所提出的分数阶混沌系统。电路仿真与数值解析结果一致,表明了所提出的两种分析方法是可行的,并证实了该分数阶混沌系统也有着复杂的非线性物理现象。     

Robust synchronization of fractional-order unified chaotic systems via linear control

A new scheme for accomplishing synchronization between two fractional-order unified chaotic systems is proposed in this paper. The scheme does not require that the nonlinear dynamics of the synchronization error system must be eliminated. Moreover, the parameter of the systems does not have to be known. A controller is a linear feedback controller, which is simple in implementation. It is designed based on an LMI condition. The LMI condition guarantees that the synchronization between the slave system and the master system is achieved. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.     

分数阶混沌系统的Simulink动态仿真及硬件设计

由于目前分数阶混沌的理论分析和硬件设计都比较烦琐,提出了分数阶混沌系统的Simulink动态仿真方法。以分数阶Jerk系统为例,根据分数阶系统方程搭建分数阶混沌系统仿真模型,可动态地观察系统变量的变化规律。仿真结果表明,分数阶混沌系统的Simulink动态仿真方法是一种切实可行的分析方法。此外,还给出了分数阶混沌系统直接进行硬件设计的方法,这为分数阶混沌系统的数字设计提供了新的思路。     

BIBO stability of fractional-order controlled nonlinear systems

The BIBO stability of fractional-order controlled nonlinear systems is investigated in this paper. By introducing the properties of some Mittag-Leffler functions and using an inequality satisfied by the Caputo derivative of a Lyapunov function, sufficient conditions to guarantee the BIBO stability are firstly presented. Then, the boundedness of solutions of the fractional financial system and the fractional low-order atmospheric circulation system are proved by the established stability results. Besides, two illustrative examples verify the theoretical results.     

时滞Chen混沌系统的指数同步及在保密通信中的应用

针对一类参数未知的时滞Chen混沌系统, 研究了其指数同步问题. 利用Lyapunov稳定理论设计了指数同步控制器和参数自适应律, 基于线性矩阵不等式技术给出了其指数同步的充分条件. 利用所提出的指数同步方法解决了保密通信问题, 且更符合实际情况. 所设计的控制器是实用有效, 易于实现. 仿真示例验证了该方法的有效性.     

分数阶超混沌系统的模糊控制和同步

采用分数阶T-S模糊模型对分数阶超混沌系统建模,采用并行分布补偿方法设计模糊控制器,通过适当设置状态反馈矩阵使得闭环极点位于稳定区域内,从而保证闭环系统满足渐近稳定性条件,通过设置同步状态反馈矩阵实现两个具有不同初始条件的分数阶Rossler超混沌系统的同步,数值仿真结果表明该方案的效果十分理想。     

基于自适应模糊逻辑系统的一类混沌系统同步控制

针对一类带有未知函数和干扰的混沌系统,进行了基于自适应模糊逻辑系统的自适应同步控制器的设计。首先基于模糊逼近原理,通过对该混沌系统中未知函数的输入输出进行采样,根据采样数据信息设计出具有参数自适应功能的Mamdani型模糊逻辑系统;然后利用该模糊逻辑系统给出一种带有参数自适应的驱动响应同步控制器设计方法;最后通过数值仿真算例表明了该方法的有效性。     

Delay-dependent consensus condition for a class of fractional-order linear multi-agent systems with input time-delay

The consensus problem of a class of fractional-order linear multi-agent systems with distributed control containing input time-delay is investigated. By adopting the frequency domain analysis and generalised Nyquist criterion for the fractional-order time-delay systems, the delay-dependent consensus condition is obtained. Then, we are interested in finding the maximum time-delay tolerance and give an exact formula for calculating the maximum time-delay to maintain the system is consensusable. As illustrated by the numerical examples, the proposed theoretical results work effectively and accurately.     

一类混沌系统的滑动模态同步控制及其应用

利用Lyapunov函数定理,设计滑动模态控制器,研究了两个相同Chen混沌系统的同步控制问题。寻找主-从Chen混沌系统满足Lyapunov稳定性理论的条件,在此基础上构造出合适的滑模控制律实现混沌系统之间的完全同步。通过数值仿真结果,证实了所设计方法的有效性和鲁棒性。结合混沌掩盖技术,将该同步方法应用于保密通信中,可以达到掩盖有用传输信号的目的,在接收端无失真地复原出发送端传送的有用信号。     

Elaboration of a generalized approach to control and to synchronize the fractional-order chaotic systems

In this paper, a new general optimal structure and parameters of the fractional-order feedback control law (OSP-FoF) is developed for controlling and synchronizing a large class of fractional-order chaotic systems (FoCS). The design of the OSP-FoF model is based on bounded-input bounded-output stabilization arguments, small gain theorem (SGT), and the matrix norms. The proposed model is theoretically rigorous and represents a powerful and simple approach which provides a reasonable trade-off between computational overhead, storage space, numerical accuracy and stability analysis for control and synchronization purposes of FoCS. Simulation results for the stabilization and synchronization of fractional-order hyperchaotic systems demonstrate the effectiveness of this newly proposed approach.     

一类非自治混沌系统的自适应脉冲同步

研究了一类具有未知Lipschitz常数的非自治混沌系统的自适应脉冲同步问题.首先基于Lyapunov稳定性理论、自适应控制理论及脉冲控制理论设计了自适应控制器、脉冲控制器及参数自适应律,然后利用推广的Barbalat引理,理论证明响应系统与驱动系统全局渐近同步,并给出了相应的充分条件.两个数值仿真例子表明本方法的有效性.