An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.

Chirp-Rate Resolution of Fractional Fourier Transform in Multi-component LFM Signal

Distinguishing close chirp-rates of different linear frequency modulation （LFM） signals under concentrated and complicated signal environment was studied. Firstly, detection and parameter estimation of multi-component LFM signal were used by discrete fast fractional Fourier transform （FrFT）. Then the expression of chirp-rate resolution in fractional Fourier domain （FrFD） was deduced from discrete normalize time-frequency distribution, when multi-component LFM signal had only one center frequency. Furthermore, the detail influence of the sampling time, sampling frequency and chirp-rate upon the resolution was analyzed by partial differential equation. Simulation results and analysis indicate that increasing the sampling time can enhance the resolution, but the influence of the sampling frequency can he omitted. What＇s more, in multi-component LFM signal, the chirp-rate resolution of FrFT is no less than a minimal value, and it mainly dependent on the biggest value of chirp-rates, with which it has an approximately positive exponential relationship.

Generalized Parseval’s Theorem on Fractional Fourier Transform for Discrete Signals and Filtering of LFM Signals

This paper investigates the generalized Parseval’s theorem of fractional Fourier transform (FRFT) for concentrated data. Also, in the framework of multiple FRFT domains, Parseval’s theorem reduces to an inequality with lower and upper bounds associated with FRFT parameters, named as generalized Parseval’s theorem by us. These results theoretically provide potential valuable applications in filtering, and examples of filtering for LFM signals in FRFT domains are demonstrated to support the derived conclusions.

Improved Speech Denoising Algorithm Based on Discrete Fractional Fourier Transform

The speech signal and noise signal are the typical non-stationary signals,however the speech signa is short-stationary synchronously.Presently,the denoising methods are always executed in frequency domain due to the short-time stationarity of the speech signal.In this article,an improved speech denoising algorithm based on discrete fractional Fourier transform（DFRFT）is pre sented.This algorithm contains linear optimal filtering and median filtering.The simulation shows that it can easily eliminate the noise compared to Wiener filtering improve the signal to noise ratio（SNR）,and enhance the original speech signal.

Decomposition of Supercritical Linear-Fractional Branching Processes

It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienayme-Galton-Watson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.

Nonlinear symbolic LFT model for UAV

A nonlinear modeling framework is presented for an oceanographic unmanned aerial vehicle （UAV） by using symbolic modeling and linear fractional transformation （LFT） techniques . Consequently, an exact nonlinear symbolic LFT model of the UAV is derived in a standard M-A form where M represents the nominal, known, part of the system and A contains the time-varying, uncertain and nonlinear components. The advantages of the proposed modeling approach are that： it not only provides an ideal starting point to obtain various final design-oriented models through subse- quent assumptions and simplifications, but also it facilitates the control system analysis with models of different levels of fidelity/complexity. Furthermore, a linearized symbolic LFT model of the UAV is proposed based on the LFT differentiation, which is amenable directly to a sophisticated linear ro- bust control strategy such as μ synthesis/analysis. Both of the derived LFT models are validated with the original nonlinear model in time domain. Simulation results show the effectiveness of the pro- posed algorithm.

基于分数阶傅里叶滤波的数字信道化储频

现代战场环境电磁日趋密集和复杂,各类信号相互混迭,同时各种相参雷达采用脉冲压缩技术以及相参处理方法,抗噪声和抗干扰能力大大增强,特别是采用线性调频(LFM)信号满足了雷达大威力、低截获的功能设计需求,抗干扰能力也得到提高。常规的数字储频(DRFM)采用宽带采集,在数字上对宽带信号进行调频、叠加等调制处理,在瞬时带宽内调制样式、参数是相同的,此处理方式导致瞬时带宽内多信号时,无法针对性施加不同的调制样式,以致干扰粗放、不够精确。为实现精确、有效的干扰相参脉冲压缩雷达,文中提出了采用频域子带处理与分数阶傅里叶滤波的数字信道化干扰设计,增强LFM信号去噪能力,通过DRFM技术形成假目标干扰信号,实施有效干扰。

Magnetic Field Analytical Model for Magnetic Harmonic Gears Using the Fractional Linear Transformation Method

Magnetic harmonic gears with high gear ratios exhibit high torque densities.However,the revolution and rotation of the eccentric rotor makes the magnetic field analysis complex.In this study,an analytical model of magnetic fields for magnetic harmonic gears is developed by using the fractional linear transformation method.The transformation formula is accurate in theory and suitable for the analysis of magnetic fields with large eccentricity.The rotor eccentricity region in the z-plane is mapped onto a uniform region in the w-plane.The magnetic field solutions are obtained by modulating the magnetic field distributions without rotor eccentricity with the relative permeance function derived from the effect of rotor eccentricity.The torque of magnetic harmonic gears is calculated from the radial and tangential components of the air-gap magnetic fields.Results of the finite element method and prototype test confirm the validity of the analytical prediction.

机器人LFT变增益H_∞控制

针对平面两关节直接驱动机器人 ,基于LMI技术提出一种设计能保证在整个运动范围内始终具有很好动态性能的LFT变增益H∞ 控制器的新方法 .将机器人系统转化为以两关节夹角余弦值为变参数的LPV模型并表示为关于变参数的LFT结构 ,利用变参数的测量值设计具有相同LFT结构的LPVH∞ 控制器 ,将此控制器的设计等价为以变参数为不确定项的LTI鲁棒控制器的设计并给出控制器可解的LMIs条件 ,然后归纳出获得控制器的求解方法 .此控制器既克服了传统变增益控制器的缺陷 ,又利用变参数的测量值降低了控制器设计的保守性 .实验结果验证了此控制器的有效性和先进性 .

基于LFT的鲁棒变增益控制的降保守性设计

研究了线性变参数系统的鲁棒变增益控制，介绍了基于LFT的鲁棒变增益控制的思想；针对目前基于LFT的鲁棒变增益控制的保守性，采用全块标量矩阵，通过减少对全块标量矩阵的结构约束；提出了一种保守性更小的稳定性判据，并且利用消元定理，给出了基于LFT的鲁棒变增益的输出反馈控制器存在的条件；同时给出了控制器的构建方式，并且给出了求解控制器的迭代LMI算法。仿真结果表明，所提方法能够得到更小的性能指标，比现有方法具有更小的保守性，验证了方法的有效性。

脉冲噪声下基于CNN-FRFT的线性调频信号参数估计方法

由于脉冲噪声破坏了线性调频(LFM)信号的分数谱特征,使得基于分数谱特征的参数估计方法无法有效估计参数。针对这个问题,提出一种脉冲噪声环境下基于CNN-FRFT的LFM信号参数估计方法。首先,利用α稳定分布拟合随机脉冲噪声,构建加性含噪信号,输入卷积神经网络(CNN)进行训练和测试;其次,利用训练好的CNN模型对信号进行去噪,并验证模型的去噪能力和泛化能力;最后,利用分数阶傅里叶变换(FRFT)建立去噪信号的分数谱,通过峰值点位置来估计LFM信号的参数。实验结果表明,相比于传统的基于非线性函数的方法,该方法在强脉冲噪声环境下具有更好的精度和噪声鲁棒性,CNN的应用使其具有更强的泛化能力,在实测脉冲噪声下仍可以准确估计参数。

基于FRFT的低信噪比LFM信号参数快速估计算法

基于分数阶傅里叶变换(Fractional Fourier Transform,FRFT)对线性调频(Linear Frequency Modulated,LFM)信号参数进行估计,问题关键是确定FRFT最佳阶数,根据误差迭代思想提出新的参数估计算法,该算法利用归一化带宽和旋转角的转化关系,由估计误差推算角度差值,有效降低了运算量,不需要调频斜率正负的先验信息,改进的对数搜索算法可以进一步提高参数估计结果的稳定性和可靠性。仿真结果表明,信噪比在-8 dB以上时该方法在高效率的前提下仍具有良好的参数估计性能,平均估计误差在1%以内,估计结果接近Cramer-Rao下限,满足工程实时处理需求。

μ ANALYSIS AND μ SYNTHESIS FOR NONLINEAR ROBUST CONTROL SYSTEMS

μＡＮＡＬＹＳＩＳＡＮＤμＳＹＮＴＨＥＳＩＳＦＯＲＮＯＮＬＩＮＥＡＲＲＯＢＵＳＴＣＯＮＴＲＯＬＳＹＳＴＥＭＳ＊ＷｕＭｉｎＰｅｎｇＺｈｉｈｏｎｇＴａｎｇＣｈａｏｈｕｉＧｕｉＷｅｉｈｕａ（ＣｏｌｅｇｅｏｆＩｎｆｏｒｍａｔｉｏｎＥｎｇｉｎｅｅｒｉｎｇ，Ｃｅ...

The concise fractional Fourier transform and its application in detection and parameter estimation of the linear frequency-modulated signal

A concise fractional Fourier transform （CFRFT） is proposed to detect the linear frequency-modulated （LFM） signal with low signal to noise ratio （SNR）. The frequency axis in time-frequency plane of the CFRFT is rotated to get the spectrum of the signal in different an- gles using chirp multiplication and Fourier transform （FT）. For LFM signal which distributes as a straight line in time-frequency plane, the CFRFT can gather the energy in the corresponding angle as a peak and improve the detection SNR, thus the LFM signal of low SNR can be de- tected. Meanwhile, the location of the peak value relates to the parameters of the LFM signal. Numerical simulations and experimental results show that, the proposed method can be used to efficiently detect the LFM signal masked by noise and to estimate the signal＇s parameters accurately. Compared with the conventional fractional Fourier transform （FRFT）, the CFRFT reduces the transform complexity and improves the real-time detection performance of LFM signal.

基于LFT-LPV结构的导弹自动驾驶仪降保守性设计

针对一类导弹纵向运动模型,提出了一种基于全块比例矩阵的LFT-LPV系统降保守性输出反馈控制器的设计方法。首先在感兴趣的飞行区域内通过数据拟合得到系统模型的LFT-LPV表示,利用S-过程,通过选择具有特定结构的全块比例矩阵避免需要在所有可能的变参数轨迹上求解无穷个LMIs的问题,同时推导出满足LFT-LPV系统性能指标的输出反馈控制器的设计方法。最后的仿真结果验证了方法的有效性。

LMI_based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.

基于FRFT的单基地MIMO雷达稳健波束形成算法

以单基地多输入多输出(multiple input multiple output,MIMO)雷达系统为研究对象,针对线性调频(linear frequency modulation,LFM)形式的正交频分复用(orthogonal frequency division multiplexing,OFDM)信号,提出了一种新的稳健自适应波束形成算法。所提算法首先利用LFM信号的特性,对匹配滤波后的雷达回波信号进行分数阶傅里叶变换(fractional Fourier transform,FRFT),经化简得到峰值点作为阵列的观测值。而后,利用观测值构建接收信号的协方差矩阵,并使用Capon谱估计方法重构干扰加噪声数据协方差矩阵。最后,通过求解优化问题估计实际导向矢量,从而得到阵列的最优权值。通过计算机仿真实验,验证了所提算法的有效性。

基于多普勒中心频率估计值的RFrFT-RD成像算法研究

针对多普勒中心频率估计值对合成孔径雷达(SAR)成像信号能量聚焦性能的影响,文中首先确立距离向分数阶傅里叶变换(FrFT)域能量聚焦轴,然后推导分析距离向分数阶傅里叶变换域能量聚焦轴与多普勒中心频率的关系式,接着构建距离向FrFT域成像算法(RFrFT-RD),最后利用星载SAR实测数据进行地物目标成像。实验结果表明,当多普勒中心频率估计值误差由0逐步增大到5%时,所提RFrFT-RD算法具有较好的成像性能稳定性。与传统的距离多普勒(RD)算法相比,所提算法距离向分辨率绝对值平均提高约7.69 m,而距离向峰值旁瓣比(PSLR)平均降低约1.88 dB,距离向积分旁瓣比(ISLR)平均降低约2.89 dB。

Mathematical Aspects of SU (2) and SO(3,R) Derived from Two-Mode Realization in Coordinate-Invariant Form

Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.

基于改进的FrFT的LFM最佳u域点滤波

分数阶傅里叶变换(Fractional Fourier Transform,FrFT)能够对线性调频信号(Linear Frequency Modulation,LFM)起到很好的能量聚焦效果,因此常用FrFT来对LFM信号进行未知参数估计以及滤波。基于此,提出了一种基于改进的FrFT的最佳u域滤波算法。仿真结果表明,相较于传统的在FrFT u域下的滤波而言,所提的滤波算法信号幅度谱损失更少,信息保留更完整,输出信噪比提升了3 dB,运算量减少了25%。