Local Bifurcation Analysis of a Delayed Fractional-order Dynamic Model of Dual Congestion Control Algorithms

In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay, the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results.      

基于自适应分数阶微分的引导滤波及其应用

引导滤波算法具有保边平滑的功能,但传统引导滤波方法容易导致图像平滑区域过度模糊、细节丢失的问题。为了使引导滤波在保持高频信息的同时结构化输出低频灰度,本文提出了一种基于自适应分数阶微分的引导滤波算法。以分数阶微分理论为基础定义了分数阶微分掩膜,并结合图像梯度、二维信息熵和局部方差权值构造了自适应分数阶微分阶数函数来有效检测图像纹理和梯度变化,从而将图像局部特性转移到引导图像中,确保在平滑去噪的同时保持图像纹理细节。实验结果表明,本文算法具有良好的边缘和纹理保持特性。另外,将本文算法运用到基于PCA和SVM的人脸识别图像预处理中,能一定程度提升人脸识别率。     

Fractional Modeling and Analysis of Coupled MR Damping System

The coupled magnetorheological (MR) damping system addressed in this paper contains rubber spring and magnetorheological damper. The device inherits the damping merits of both the rubber spring and the magnetorheological damper. Here a fractional-order constitutive equation is introduced to study the viscoelasticity of the combined damper. An introduction to the definitions of fractional calculus, and the transfer function representation of a fractional-order system are given. The fractional-order system model of a magnetorheological vibration platform is set up using fractional calculus, and the function of displacement is presented. It is indicated that the fractional-order constitutive equation and the transfer function are feasible and effective means for investigating of magnetorheological vibration device.      

Arbitrary-Order Fractance Approximation Circuits With High Order-Stability Characteristic and Wider Approximation Frequency Bandwidth

This paper discusses a novel rational approximation algorithm of arbitrary-order fractances, which has high order-stability characteristic and wider approximation frequency bandwidth. The fractor has been exploited extensively in various scientific domains. The well-known shortcoming of the existing fractance approximation circuits, such as the oscillation phenomena, is still in great need of special research attention. Motivated by this need, a novel algorithm with high order-stability characteristic and wider approximation frequency bandwidth is introduced. In order to better understand the iterating process, the approximation principle of this algorithm is investigated at first. Next, features of the iterating function and frequency-domain characteristics of the impedance function calculated by this algorithm are researched, respectively. Furthermore, approximation performance comparisons have been made between the corresponding circuit and other types of fractance approximation circuits. Finally, a fractance approximation circuit with the impedance function of negative 2/3-order is designed. The high order-stability characteristic and wider approximation frequency bandwidth are fundamental important advantages, which make our proposed algorithm competitive in practical applications.      

Distributed Adaptive Cooperative Tracking of Uncertain Nonlinear Fractional-order Multi-agent Systems

In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws, we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result.      

基于分数阶全变差和自适应正则化参数的图像去模糊

为更好地复原图像的纹理细节,避免求解图像去模糊模型时面临正则化参数难以选择的问题,提出了一种基于分数阶全变差（FOTV）模型和自适应更新正则化参数的非盲去模糊图像重建方法。首先,在分析不同分数阶下FOTV的幅频响应特性的基础上,采用不同分数阶次的FOTV模型约束图像的平滑（低频）部分和纹理细节（高频）部分,从而建立图像非盲去模糊重建模型。其次,为了有效地求解重建模型和实现两个正则化参数的自适应更新,采用交替方向乘子法(ADMM)将原本含有两个正则化参数的复杂问题分解成两个相对容易的子问题进行求解,每个子问题只含一个正则化参数。最后,根据偏差准则,在迭代求解过程中实现了两个正则化参数的自适应更新。将所提算法应用于包含平滑、边缘和纹理细节的多幅图像中,测试4种不同模糊核下的去模糊效果;与传统的4种去模糊算法相比,实验结果表明所提算法能自适应地更新两个正则化参数,对于纹理细节适中的图像具有较好的去模糊效果。     

一类分数阶冠状动脉系统的混沌同步控制

基于Lyapunov稳定性理论和分数阶微积分,研究一类分数阶冠状动脉系统的混沌同步问题,给出系统取得同步的三个充分性条件。研究表明:选取适当的控制器,系统能够取得混沌同步。     

Partial fraction expansion–based realizations of fractional-order differentiators and integrators using active filters

Approximations of the fractional-order differentiator and integrator operators s^±r are proposed in this work. These approximations target the realization of these operators using standard active filter transfer functions. Hence, circuit implementations in integrated circuit form or in discrete component form are significantly facilitated. Complementary metal-oxide-semiconductor (CMOS) realizations of the proposed approximations are given and validated via simulations using the AMS 0.35 μm CMOS technology, while experimental results using operational amplifier circuits are tested and confirm the proposed theory.     

分数阶Rossler混沌系统的模糊同步控制

采用分数阶T-S模糊模型对分数阶Rossler混沌系统建模．使用并行分布式补偿方法设计模糊状态反馈控制器,使得闭环系统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．利用所设计的模糊状态反馈同步控制器实现了两个具有不同初始条件的分数阶Rossler混沌系统的同步．数值仿真结果表明该方案的有效性．     

Observer-based quasi-containment of fractional-order multi-agent systems via event-triggered strategy

This paper is devoted to the quasi-containment control problem of fractional-order multi-agent systems (FOMASs). First, to reduce the frequency of communications, a novel observer-based event-triggered control mechanism which only relies on the information at the trigger-time is proposed. And then, by applying the theory of algebraic graph, matrix and fractional-order calculus, some sufficient consensus conditions based on the linear matrix inequality are established for achieving the consensus of FOMASs. In addition, the strict positive lower bound on the inter-event interval is obtained, which implies that the system is free from the Zeno behaviour. Finally, several simulation examples are presented to demonstrate the effectiveness of the theoretical results.