分数阶记忆元件通用等效电路的设计

根据分数阶记忆元件之间的转换关系,设计了一种分数阶记忆元件通用等效电路。该等效电路在不改变电路拓扑结构的情况下,通过选择五个阻抗元件的类型,可以将任意一种接地型分数阶记忆元件转换为任意一种浮地型分数阶记忆元件。在仿真实验中,根据提出的通用等效电路,分别实现了三种分数阶记忆元件。对三种分数阶记忆元件的特性进行了分析,验证了该等效电路的正确性。     

Order-dependent and delay-dependent conditions for stability and stabilization of fractional-order time-varying delay systems using small gain theorem

In this paper, the stability and stabilization problems for fractional-order time-varying delay systems are investigated. Firstly, by casting the stability problem as one of robust stability analysis problems and utilizing the small gain theorem, an order-dependent and delay-dependent stability condition for fractional-order time-varying delay systems is developed. Taking advantage of the information of order and delay, the stability condition is less conservative than the existing results. Then, state feedback controllers that stabilize fractional-order time-varying delay systems are developed. To tackle the computational difficulty of the controller design method, a local optimization algorithm is proposed. Finally, numerical examples are provided to illustrate that the proposed criteria are valid and less conservative than the existing ones.     

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。     

Sliding Mode Control of Fractional-Order Memristive System

A sliding mode controller for a fractional-order memristor-based chaotic system is designed to address its problem in stabilization control. Firstly, a physically realizable fractional-order memristive chaotic system was introduced, which can generate a complex dynamic behavior. Secondly, a sliding mode controller based on sliding mode theory along with Lyapunov stability theory was designed to guarantee the occurrence of the sliding motion. Furthermore, in order to demonstrate the feasibility of the controller, a condition was derived with the designed controller''s parameters, and the stability analysis of the controlled system was tested. A theoretical analysis shows that, under suitable condition, the fractional-order memristive system with a sliding mode controller comes to a steady state. Finally, numerical simulations are shown to verify the theoretical analysis. It is shown that the proposed sliding mode method exhibits a considerable improvement in its applications in a fractional-order memristive system.     

分数阶PID模型预测控制算法改进研究

在分析FOPID(分数阶PID)算法和MAC(模型算法控制)算法的基础上,结合两种算法的优点,推导了基于FOPID性能指标的改进的MAC控制算法FOPID-MAC算法.这种算法既具有FOND算法的优点,稳定性较好,又具有预测功能.通过仿真研究的对比,在时域内分析了FOPID-MAC控制器的参数选择对系统控制性能的影响,...     

Parameter Estimation and Topology Identification of Uncertain General Fractional-order Complex Dynamical Networks with Time Delay

Complex networks have attracted much attention from various fields of sciences and engineering in recent years. However, many complex networks have various uncertain information, such as unknown or uncertain system parameters and topological structure, which greatly affects the system dynamics. Thus, the parameter estimation and structure identification problem has theoretical and practical importance for uncertain complex dynamical networks. This paper investigates identification of unknown system parameters and network topologies in uncertain fractional-order complex network with time delays (including coupling delay and node delay). Based on the stability theorem of fractional-order differential system and the adaptive control technique, a novel and general method is proposed to address this challenge. Finally two representative examples are given to verify the effectiveness of the proposed approach.      

基于非线性牵制控制的分数阶混沌网络聚同步

针对分数阶混沌复杂网络,提出一种非线性牵制控制策略实现网络聚同步.根据网络结点的不同属性,只对群间点施加非线性控制,然后基于分数阶系统稳定性理论,给出了实现聚同步的充分条件.数值仿真验证了该聚同步方案的有效性和正确性,同时深入讨论了控制增益和耦合强度等对聚同步的影响.     

频域法在分数阶混沌系统计算中的局限性分析

基于分数阶积分算子在频域内的响应,分析了频域近似法在分数阶混沌系统计算中的局限性.频域近似法只能在期望的频带范围内实现与实际系统的近似,而在高频与低频段都存在着较大的误差.因此,当其应用到分数阶混沌系统计算时存在着很大的局限性,甚至得到与预估-校正算法完全不同的结论.通过对分数阶Chen系统的仿真,验证了该结论的正确性.     

自适应分数阶变分去泊松噪声新模型

目的 针对传统总变分方法在去除泊松噪声时容易出现“阶梯效应”和图像边缘模糊的问题,提出了一种基于分数阶变分的自适应去泊松噪声新模型。方法 首先新模型在分析了泊松噪声分布特点的基础上导出了非凸自适应正则项,它能够根据图像不同区域的特点自适应地调节正则项系数,以达到保持图像边缘的目的。然后,新模型利用分数阶离散微分向量能够结合更多图像信息的特点,将正则项中的一阶离散微分向量替换为分数阶离散微分向量,以此来达到抑制“阶梯效应”的目的。对于新模型的求解,结合交替迭代法和加权原始-对偶法提出了一种高效的数值解法。结果 新模型明显优于传统总变分去泊松噪声模型,在有效抑制“阶梯效应”的同时图像边缘也得到了较好地保护,以经典的Peppers图片为例,新模型相比于传统模型,峰值信噪比（PSNR）由28.98 dB提高到了30.24 dB,图像结构相似度（SSIM）由0.77提高到了0.87。另外,所提的数值解法具有收敛速度快、复杂度低的特点,收敛时间从偏微分方程、Chambolle投影等传统数值解法的0.5 s与0.1 s缩短至0.056 s。结论 实验结果表明,所提模型与数值解法的可行性,模型与数值解法在主要客观评价指标和图像视觉效果方面均优于传统的变分去泊松噪声模型,且模型与数值解法具有较好的普适性。但是模型中分数阶的阶次选取有待进一步优化。     

Artificial Bee Colony Algorithm-based Parameter Estimation of Fractional-order Chaotic System with Time Delay

It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well as system's parameters are concerned by treating the time delay and fractional order as additional parameters. The parameter estimation is converted into a multi-dimensional optimization problem. A new scheme based on artificial bee colony (ABC) algorithm is proposed to solve the optimization problem. Numerical experiments are performed on two typical time-delay fractional-order chaotic systems to verify the effectiveness of the proposed method.