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。     

建筑结构含分数阶振动控制的最优阶次研究

为了在实际控制中获得更好的控制效果,以整数阶模型为研究对象,在控制器设计时人为地引入分数阶,通过定义控制性能指标和寻优来确定最优控制的分数阶阶次.为了建立分数阶系统和原整数阶系统之间的联系,取含分数阶状态方程和原整数阶系统状态方程一致的输出变量,并采用输出控制策略使得所设计的分数阶控制器能够应用于原整数阶模型.仿真结果表明,分数阶阶次的选择不仅影响系统控制的效果,还影响系统的稳定性,并给出了一个实例分析来说明本研究方法的可行性.     

分数阶混沌系统的广义同步研究

研究基于分数阶稳定性理论,构造出一个恰当的耦合矩阵,建立分数阶混沌响应系统,使得分数阶混沌系统实现广义同步．以一个改进的分数阶Rikitake混沌系统的广义同步为例进行仿真研究,数值结果表明该广义同步方法的有效性和可行性．     

Dynamic Analysis of Fractional-Order Memristive Chaotic System

分数阶忆阻器混沌电路的动力学分析

丁大为,李书家,王年

(安徽大学 电子信息工程学院,合肥 230601)

中文说明：

为研究系统的非线性动力学,提出一个从相对应的整数阶演变而来的分数阶忆阻蔡氏电路。首先,根据李亚普诺夫间接法,对分数阶忆阻系统的稳定性进行分析,结果表明：当忆阻系统的分数阶参数达到临界值时,系统失去稳定性,并发生分岔。然后,根据不同分数阶阶数以及不同其他系统参数的分岔图表明分数阶忆阻系统发生分岔和混沌行为。此外,为证明分数阶忆阻混沌系统存在混沌行为,给出了系统的时域图、相位图和最大的李亚普诺夫指数图。最后,通过数值仿真说明和验证理论结果的正确性。

关键词：忆阻器;动力学行为;分数阶;稳定性

     

具有纠缠项的分数阶五维混沌系统滑模同步的两种方法

根据滑模和积分滑模两种方法研究具有3个纠缠项的分数阶五维混沌系统的滑模同步,给出滑模面和控制器的两种设计方法,得到纠缠混沌系统取得滑模同步的2个充分条件。研究表明:一定条件下,分数阶五维纠缠混沌系统取得滑模同步。通过数值仿真,验证了控制器的正确定性和有效性。     

基于自适应模糊滑模控制的分数阶混沌系统的投影同步

基于模糊控制理论和滑模控制理论以及自适应控制理论,研究了一类含有外部扰动的不确定分数阶混沌系统的混合投影同步问题.提出了一种自适应模糊滑模控制的分数阶混沌系统投影同步方法.模糊逻辑系统用来逼近未知的非线性函数和外部扰动,并且对逼近误差采用了自适应控制,同时构造了一种具有较强鲁棒性的分数阶积分滑模面.应用分数阶Barbalat引理设计了自适应模糊滑模控制器和参数自适应律.最后数值仿真结果验证了所提控制方法的有效性.     

Containment Control of Fractional Order Multi-Agent Systems With Time Delays

In complex environments, many distributed multiagent systems are described with the fractional-order dynamics. In this paper, containment control of fractional-order multiagent systems with multiple leader agents are studied. Firstly, the collaborative control of fractional-order multi-agent systems (FOMAS) with multiple leaders is analyzed in a directed network without delays. Then, by using Laplace transform and frequency domain theorem, containment consensus of networked FOMAS with time delays is investigated in an undirected network, and a critical value of delays is obtained to ensure the containment consensus of FOMAS. Finally, numerical simulations are shown to verify the results.      

Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay

This paper investigates the finite-time stability problem of a class of nonlinear fractional-order system with the discrete time delay. Employing the Laplace transform, the Mittag-Leffler function and the generalised Gronwall inequality, the new criterions are derived to guarantee the finite-time stability of the system with the fractional-order 0 < α < 1. Further, we propose the sufficient conditions for ensuring the finite-time stability of the system with the fractional-order 1 < α < 2. Finally, based on the modified Adams–Bashforth–Moulton algorithm for solving fractional-order differential equations with the time delay, we carry out the numerical simulations to demonstrate the effectiveness of the proposed results, and calculate the estimated time of the finite-time stability.     

Consensus with a reference state for fractional-order multi-agent systems

This paper investigates consensus of fractional-order multi-agent systems (MASs) with a reference state. First, a consensus control law with a constant reference state is given using graph theory and stability analysis of fractional-order. Then, a general control law and a particular one for consensus of fractional-order MASs with a time-varying reference state are proposed. Next, the above control laws are extended to solve formation tracking problem. Finally, several simulations are presented to verify the effectiveness of the obtained results.