集成神经网络与自适应算法的分数阶滑模控制

针对被控对象的参数时变和外部扰动问题,本文融合神经网络的万能逼近能力和自适应控制技术,并结合分数阶微积分理论,提出了基于神经网络和自适应控制算法的分数阶滑模控制策略.本文采用等效控制的方法设计滑模控制律,并利用神经网络的万能逼近能力估测控制律的变化,结合自适应控制算法和分数阶微积分理论抑制传统滑模控制系统的抖震,同时根据Lyapunov稳定性理论分析了系统的稳定性,最后给出了实验结果.实验结果表明,本文提出的基于神经网络和自适应控制算法的分数阶滑模控制系统,能保持滑模控制器对系统外部扰动和参数变化鲁棒性的同时,也能有效地抑制抖震,使得系统获得较高的控制性能.     

基于稀疏PCA的多阶次分数阶傅里叶变换域特征人脸识别

文章提出基于稀疏PCA的多阶次分数阶傅里叶变换(fractional Fourier features,Frft)特征的人脸识别(Multiple Order discrete fractional Fourier Features ,MOFF). 鉴于分数阶傅里叶变换对光照、表情的鲁棒性, 并已在图像处理领域得到应用,首先,Frft幅度随阶次的变换呈现压缩性,而SPCA提取其主要信息将且分为主要信息域和次要信息域,融合二者的互补信息组成混合幅度特征,然后融合混合幅度特征、实部特征和虚部特征,最后融合不同阶次下Frft域特征。此外该文提出基于贪婪算法的分数阶阶次选择算法和基于Fisherfaces的权重方法。ORL 和AR人脸数据库上的仿真证明了本算法的有效性。     

A Galerkin finite element scheme for time–space fractional diffusion equation

In this paper, a Galerkin finite element scheme to approximate the time–space fractional diffusion equation is studied. Firstly, the fractional diffusion equation is transformed into a fractional Volterra integro-differential equation. And a second-order fractional trapezoidal formula is used to approach the time fractional integral. Then a Galerkin finite element method is introduced in space direction, where the semi-discretization scheme and fully discrete scheme are given separately. The stability analysis of semi-discretization scheme is discussed in detail. Furthermore, convergence analysis of semi-discretization scheme and fully discrete scheme are given in details. Finally, two numerical examples are displayed to demonstrate the effectiveness of the proposed method.     

Simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise

In the present paper, the identification and estimation problem of a single-input–single-output (SISO) fractional order state-space system will be addressed. A SISO state-space model is considered in which parameters and also state variables should be estimated. The canonical fractional order state-space system will be transformed into a regression equation by using a linear transformation and a shift operator that are appropriate for identification. The identification method provided in this paper is based on a recursive identification algorithm that has the capability of identifying the parameters of fractional order state-space system recursively. Another subject that will be addressed in this paper is a novel fractional order Kalman filter suitable for the systems with coloured measurement noise. The promising performance of the proposed methods is verified using two stable fractional order systems.     

Subspace-based continuous-time identification of fractional order systems from non-uniformly sampled data

This work focuses on the identification of fractional commensurate order systems from non-uniformly sampled data. A novel scheme is proposed to solve such problem. In this scheme, the non-uniformly sampled data are first complemented by using fractional Laguerre generating functions. Then, the multivariable output error state space method is employed to identify the relevant system parameters. Moreover, an in-depth property analysis of the proposed scheme is provided. A numerical example is investigated to illustrate the effectiveness of the proposed method.     

Condition-based diagnosis of mechatronic systems using a fractional calculus approach

While fractional calculus (FC) is as old as integer calculus, its application has been mainly restricted to mathematics. However, many real systems are better described using FC equations than with integer models. FC is a suitable tool for describing systems characterised by their fractal nature, long-term memory and chaotic behaviour. It is a promising methodology for failure analysis and modelling, since the behaviour of a failing system depends on factors that increase the model’s complexity. This paper explores the proficiency of FC in modelling complex behaviour by tuning only a few parameters. This work proposes a novel two-step strategy for diagnosis, first modelling common failure conditions and, second, by comparing these models with real machine signals and using the difference to feed a computational classifier. Our proposal is validated using an electrical motor coupled with a mechanical gear reducer.     

Output feedback control of linear fractional transformation systems subject to actuator saturation

In this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.     

Robust Estimation of GARMA Model Parameters with an Application to Cointegration among Interest Rates of Industrialized Countries

We review the literature on long memory ARFIMA and GARMA models andintroduce a new efficient estimator for GARMA models, which we show to berobust. Next we conduct a Monte Carlo study to demonstate the power of theDickie–Fuller test when the data are generated from a stationary GARMAprocess. We conclude with a brief discussion of cointegration in the contextof GARMA models with an application to international interest rates.