A proof for non existence of periodic solutions in time invariant fractional order systems

The aim of this note is to highlight one of the basic differences between fractional order and integer order systems. It is analytically shown that a time invariant fractional order system contrary to its integer order counterpart cannot generate exactly periodic signals. As a result, a limit cycle cannot be expected in the solution of these systems. Our investigation is based on Caputo’s definition of the fractional order derivative and includes both the commensurate or incommensurate fractional order systems.     

Fractional order [proportional derivative] controller for a class of fractional order systems

Recently, fractional order systems (FOS) have attracted more and more attention in various fields. But the control design techniques available for the FOS suffer from the lack of direct systematic approaches. In this paper, we focus on a given type of simple model of FOS. A fractional order [proportional derivative] (FO-[PD]) controller is proposed for this class of FOS, and a practical and systematic tuning procedure has been developed for the proposed FO-[PD] controller synthesis. The fairness issue in comparing with other controllers such as the traditional integer order PID (IO-PID) controller and the fractional order proportional derivative (FO-PD) controller has been addressed under the same number of design parameters and the same specifications. Fair comparisons of the three controllers (i.e., IO-PID, FO-PD and FO-[PD]) via the simulation tests illustrate that, the IO-PID controller designed may not always be stabilizing to achieve flat-phase specification while both FO-PD and FO-[PD] controllers designed are always stabilizing. Furthermore, the proposed FO-[PD] controller outperforms FO-PD controller for the class of fractional order systems.     

Mittag-Leffler stability of fractional order nonlinear dynamic systems

In this paper, we propose the definition of Mittag-Leffler stability and introduce the fractional Lyapunov direct method. Fractional comparison principle is introduced and the application of Riemann-Liouville fractional order systems is extended by using Caputo fractional order systems. Two illustrative examples are provided to illustrate the proposed stability notion.     

Fractional dynamical model for the generation of ECG like signals from filtered coupled Van-der Pol oscillators

In this paper, an incommensurate fractional order (FO) model has been proposed to generate ECG like waveforms. Earlier investigation of ECG like waveform generation is based on two identical Van-der Pol (VdP) family of oscillators, which are coupled by time delays and gains. In this paper, we suitably modify the three state equations corresponding to the nonlinear cross-product of states, time delay coupling of the two oscillators and low-pass filtering, using the concept of fractional derivatives. Our results show that a wide variety of ECG like waveforms can be simulated from the proposed generalized models, characterizing heart conditions under different physiological conditions. Such generalization of the modelling of ECG waveforms may be useful to understand the physiological process behind ECG signal generation in normal and abnormal heart conditions. Along with the proposed FO models, an optimization based approach is also presented to estimate the VdP oscillator parameters for representing a realistic ECG like signal.     

Stabilization of some fractional delay systems of neutral type

In this note, we give new stability tests which enable one to fully characterize the H_∞-stability of systems with transfer function , where h>0 and p,q,r are real polynomials in the variable s^μ for 0<μ<1.As an application of this, in the case r(s)=1 and degp=degq=1, families of H_∞-stabilizing controllers are given and a complete parametrization of all H_∞-stabilizing controllers is obtained when .     

光敏剂二氢卟吩e_6系列衍生物δ位取代基效应的理论研究

以含时密度泛函方法(TDDFT)结合LSDA/6-31G*方法计算二氢卟吩e6和二氢卟吩e6-C7单甲酯衍牛物的电子光谱,研究二氧卟吩母环δ位碳上取代基对电子光谱的影响.结果表明在二氢卟吩母环8位碳上引入4种取代基团(-NH2、-CH=CH2、-CHO、-NO2)后,衍生物的λmax均有较大程度的红移,δ位取代基各原子的净电荷之和QR与λmx呈高度负相关,且取代基团所带的负电荷越大,红移越显著.     

Scale Dependency of Image Derivatives for Feature Measurement in Curvilinear Structures

Extraction of image features is a crucial step in many image analysis tasks. In feature extraction methods Gaussian derivative kernels are frequently utilized. Blurring of the image due to convolution with these kernels gives rise to feature measures different from the intended value in the original image. We propose to solve this problem by explicitly modeling the scale dependency of derivatives combined with measurement of derivatives at multiple scales. This approach is illustrated in methods for feature measurement in curvilinear structures. Results in 3D Confocal Images confirm that modelling of scale behavior of derivatives results in improved methods for center line localization in curved line structures and enables curvature and diameter measurement.     

一种遥感图象的混合多尺度Hurst参数分类模型

针对遥感图象分类较困难的问题,提出了一个遥感图象的分类模型－扩展的自相似模型（ESS）,该模型是一种广义的分形布朗模型（fBm),它的多尺度Hurst参数与粗糙度之间的是对应的,同时不必像分形维数那样要求粗工的尺度不变性,因而比fBm更接近于实际情况,另外,由于它的参数可以作为很好的分类特征,而且特征给数低,计算快,其方向性Hurst参数还描述了纹理在4个方向上的粗糙度,因此可将它们与灰度的均值和标准差一起作为一组特征,来构造一个混合多尺度Hurst参数分类模型,将其用于卫星遥感图象分类,获得了较高的分类正确率。     

Assessing changes of forest area and shrub encroachment in a mire ecosystem using digital surface models and CIR aerial images

This paper presents an approach to assess increase and decrease (2002–1997) of forest area and other wooded areas in a mire biotope in the Pre-alpine zone of Central Switzerland using logistic regression models and airborne remote sensing data (CIR aerial images, DSM derived from them). The present study was carried out in the framework of the Swiss Mire Protection Program, where increase and decrease of forest areas are key issues. In a first step, automatic DSMs were generated using an image matching approach from CIR aerial images of 1997 and 2002. In a second step, the DSMs were co-registered and normalized using LiDAR data. Tree layers from both years of various levels of detail were then generated combining canopy covers derived from normalized DSMs with a multi-resolution segmentation and a fuzzy classification. On the basis of these tree layers, fractional tree/shrub covers were calculated using explanatory variables derived from these DSMs only. Bias was estimated by analysing the distribution of the fractional model differences. The corrected models reveal a decrease of tree/shrub probability which indicates a decrease of forest and other wooded areas between 1997 and 2002. The models also indicate real shrub encroachment in open mire. The detection of shrub encroachment may be helpful for selective logging purposes for sustainable mire habitat management. The study stresses the importance of high-resolution and high-quality DSMs and highlights the potential of fractional covers for ecological modeling.     

Tuning and auto-tuning of fractional order controllers for industry applications

This paper deals with the design of fractional order PI^λD^μ controllers, in which the orders of the integral and derivative parts, λ and μ, respectively, are fractional. The purpose is to take advantage of the introduction of these two parameters and fulfill additional specifications of design, ensuring a robust performance of the controlled system with respect to gain variations and noise. A method for tuning the PI^λD^μ controller is proposed in this paper to fulfill five different design specifications. Experimental results show that the requirements are totally met for the platform to be controlled. Besides, this paper proposes an auto-tuning method for this kind of controller. Specifications of gain crossover frequency and phase margin are fulfilled, together with the iso-damping property of the time response of the system. Experimental results are given to illustrate the effectiveness of this method.