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

     

基于半实物仿真技术的分数阶PID控制器

采用半实物仿真技术获得被控对象特性,进而得出系统传递函数。在此基础之上采用分数阶控制器的设计算法设计系统的分数阶控制器。并将该控制器与经典PID控制器进行仿真对比,结果表明：分数阶PID控制器较传统PID控制器,在对系统响应时间的调节上取得了较好的效果。     

A Fractional Drift Diffusion Model for Organic Semiconductor Devices

Because charge carriers of many organic semiconductors (OSCs) exhibit fractional drift diffusion (Fr-DD) transport properties, the need to develop a Fr-DD model solver becomes more apparent. However, the current research on solving the governing equations of the Fr-DD model is practically nonexistent. In this paper, an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices. The Fr-DD model is composed of two fractional-order carriers (i.e., electrons and holes) continuity equations coupled with Poisson’s equation. By treating the current density as constants within each pair of consecutive grid nodes, a linear Caputo’s fractional-order ordinary differential equation (FrODE) can be produced, and its analytic solution gives an approximation to the carrier concentration. The convergence of the solver is guaranteed by implementing a successive over-relaxation (SOR) mechanism on each loop of Gummel’s iteration. Based on our derivations, it can be shown that the Scharfetter–Gummel discretization method is essentially a special case of our scheme. In addition, the consistency and convergence of the two core algorithms are proved, with three numerical examples designed to demonstrate the accuracy and computational performance of this solver. Finally, we validate the Fr-DD model for a steady-state organic field effect transistor (OFET) by fitting the simulated transconductance and output curves to the experimental data.     

基于云计算模型的分数阶超混沌加密算法

针对大数据安全以及混沌加密安全性等问题,提出了一种基于云计算模型的分数阶超混沌系统的加密算法。首先选取了两个分数阶超混沌系统的初始值作为密钥参数,基于分数阶混沌生成用于加密的伪随机序列,进而提出了一个结合云计算MapReduce并行数据处理模型的加密算法。在MapReduce并行加密方面,依次进行分块、Map并行加密和Reduce数据归并等操作。为了抵御明文类的密码攻击,算法中采用与明文特征关联的混沌序列生成方法。最后,在云计算实验环境中的实验结果表明,该算法的密钥空间达到372 bit,能够有效抵御明文类的密码攻击,具有密钥高度敏感的特性。同时,实验结果验证了云计算MapReduce并行加密的有效性。     

Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control

In this paper, the leader-following consensus problem of fractional-order multi-agent systems is considered via adaptive pinning control. The dynamics of leader and all followers with linear and nonlinear functions are investigated, respectively. We assume that the node should be pinned if its in-degree is less than its out-degree in the paper. Under this assumption and based on the stability theory of fractional-order differential systems, some leader-following consensus criteria are derived, which are easily obtained by matrix inequalities. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented. The design technique is based on algebraic graph theory and the Riccati inequality. Several simulation examples are presented to demonstrate the effectiveness of the proposed method.     

Stabilisability analysis of high-order unstable processes by fractional-order controllers

In this article, the sufficient stabilisability criteria for unstable time-delay processes by fractional-order controllers are investigated. The process is a high-order system with a single unstable pole, which also has a stable zero. The adopted approach to derive the sufficient conditions for stability is based on the well-known Nyquist stability criterion. Stabilisability is studied by applying fractional-order proportional integral and proportional derivative controllers and the results are given in terms of the maximum allowable value of time delay. Additionally, limitations on the parameters of the controllers which must be taken into account in the controller design are proposed.     

Distributed formation control of fractional-order multi-agent systems with absolute damping and communication delay

The distributed formation control of fractional-order multi-agent systems is mainly studied under directed interaction topology in this paper. First, the control algorithm with absolute damping and communication delay is proposed to achieve the formation control. Then, some sufficient conditions are derived by using the matrix theory, graph theory and the frequency-domain analysis method. Finally, based on the numerical method of predictor–corrector, several simulations are presented to illustrate the effectiveness of the obtained results.     

Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

This paper investigates the robust consensus control problem of heterogeneous unknown nonlinear fractional-order multi-agent systems (FOMASs) without leader and with multiple leaders of bounded inputs. More specifically, FOMASs with nonidentical unknown coupling nonlinearities and external disturbances are considered in this paper, which takes the first-order MASs as its special case. Based on the σ-modification adaptive control technique, some class of discontinuous robust adaptive control protocols are proposed to solve the leaderless consensus problem and containment consensus problem, respectively. By means of the set-valued maps theory and by artfully choosing Lyapunov function, it is shown that the proposed consensus protocols are user friendly in that they are capable of compensating uncertain coupling nonlinearities, rejecting disturbances, rendering smaller control gains and thus requiring smaller amplitude on the control input while preserving global consensus convergence. All of the proposed robust adaptive consensus protocols are independent of any global and unknown information and thus are fully distributed. Some numerical simulations are provided to validate the correctness of the obtained results.