基于Legendre多项式的随机连续系统的Markov参数估计

本文在讨论连续Ｗｉｓｅｎｒ过程的Ｌｅｇｅｎｄｒｅ多项式逼近值的相关性和Ｗｉｅｎｅｒ过程扰动下连续线性系统基于该正交多项的最小二乘估计有偏性后，提出了无偏一致的且数估计误差方差最小的Ｍａｒｋｏｖ估计（最小方差估计）算法，并给出本文方法的仿真结果。     

基于向量Lyapunov函数方法的模糊控制系统稳定性分析和设计

采用模糊动态模型对连续时间非线性系统进行模糊控制,对闭环模糊系统的稳定性进行分析,并给出系统化的控制器设计程序,在一系列局部模型通过模糊隶属函数连接得到的连续的全局模型中,全面考虑其它关联子系统对标称线性系统的摄动,并利用向量Lyapunov函数的概念和方法,得到了闭环模糊系统稳定的充分条件;仿真例子验证了该设计方法的正确性。     

一种基于多分辨分析的脉冲响应辨识方法

提出了一种基于正交基展开方法的脉冲响应辨识方法--正交尺度变换法.这种 方法以正交尺度函数展开的形式表示脉冲响应函数,对信号进行正交尺度变换,并使用最小 二乘类参数辨识方法估计参数.仿真结果验证了理论的正确性和方法的可行性.     

基于脉冲响应函数的正交小波变换系数的故障检测方法

提出了一种基于连续系统脉冲响应函数的正交小波变换系统的故障检测方法。该方法无需对象的数学模型,具有计算量小、故障判决过程简单、实时性较好等优点。     

基于固定尺度正交小波包变换的脉冲响应辨识方法研究

小波包变换能作为一种有效工具对信号特性进行精细分析,同时提供具有良好时频局 部性的正交小波包基.本文将Eykhoff脉冲响应辨识方法中的正交函数基取成正交小波基函数, 提出了一种新的脉冲响应辨识方法,该方法不但保证了原来Eykhoff方法的有效性,而且实用性 更好、实用范围更广.仿真结果表明,所提出的脉冲响应辨识算法对于确定性过程和随机过程都具 有很好的辨识结果,具有辨识精度高、克服噪声干扰能力和跟踪系统动态特性变化能力强的优点.     

一类用于连续过程逼近的过程神经元网络及其应用

针对实际系统的输入输出是与时间有关的连续过程,提出了一类用于连续过程逼近的过程神经元网络模型.模型利用神经网络所具有的非线性映射能力,实现系统输入输出之间的连续映射关系.考虑过程神经网络计算的复杂性,在输入空间中选择一组函数正交基,将输入函数和网络权函数表示为该组正交基的展开形式,利用基函数的正交性,简化过程神经元计算.文中给出了学习算法,并以油藏开发三次采油过程模.     

时延线性系统最优控制的一种新方法Fourier级数法

本文提出了一种用Fourier级数来分析时延线性系统的最优控制问题的新方法，通过把系统变量展开成Forrier级数，并引入了时延分析方法，以及乘法特性和正特性，将最优控制问题转化成了一个代数问题，算潮具有规范性，由于Fourier级数是一种完备的正交函数，具有较快的收敛速度和更精确的运算矩阵，所以后Fourier级数来分极时延系统最优控制问题其它正交函数（如walsh和BPFS等）有更高的精确度。     

广义线性系统的H2性能分析

利用广义Lyapunov方程,研究广义连续线性系统的稳定性,给出了一个充要条件.基于该Lyapunov方程,给出了计算广义连续线性系统的H2范数的状态空间方法.     

广义线性系统的H2性能分析

利用广义Lyapunov方程,研究广义连续线性系统的稳定性,给出了一个充分条件。基于该Lyapunov方程,给出了计算广义连续线性系统的H2范数的状态空间方法。     

脉冲响应模型的闭环子空间辨识方法

针对实际情况中难以采集控制系统开环数据的问题，对脉冲响应模型的闭环辨识问题进行了研究，提出了一种基于正交分解理论的脉冲响应模型闭环子空间辨识方法。通过使用正交分解得到联合输入输出信号的确定部分（Deterministic Components），把闭环问题转化成开环问题。利用Toeplitz矩阵下三角结构形式，对由脉冲响应模型系数组成的子空间矩阵分块分解，通过求取子空间矩阵元素的平均值来获取脉冲响应模型参数的估计。通过采用PID控制器的单输入单输出（SISO）数值仿真、多输入多输出（MIMO）数值仿真和Wood-Berry蒸馏过程仿真实验3个仿真实例，对比研究了所提方法与PBSID_OPT、CVA三种方法。仿真结果表明了所提出的方法具有良好的辨识性能。对于实际工业过程的建模问题，该研究所提的闭环子空间辨识方法具有实际的参考价值和一定的指导意义。     

Identification of linear systems using polynomial kernels in the frequency domain

In prior work we presented an identification algorithm using polynomials in the time domain. In this article, we extend this algorithm to include polynomials in the frequency domain. A polynomial is used to represent the imaginary part of the Fourier transform of the impulse response. The Hilbert transform relationship is used to compute the real part of the frequency response and hence the complete process model. The polynomial parameters are computed based on the computationally efficient linear least square method. The order of the polynomial is estimated based on residue decrement. Simulated and experimental results show the effectiveness of this method, particularly for short input/output data sequence with high signal to noise ratio. The frequency domain polynomial model complements the time domain methods since it can provide a good estimate of the time to steady state for time domain FIR (finite impulse response) models. Confidence limits in time or frequency domain can be computed using this approach. Noise rejection properties of the algorithm are illustrated using data from both simulated and real processes.     

迭代学习控制在线性时变系统终端控制问题中的应用研究

An iterative learning control algorithm based on shifted Legendre orthogonal polynomials is proposed to address the terminal control problem of linear time-varying systems. First, the method parameterizes a linear time-varying system by using shifted Legendre polynomials approximation. Then, an approximated model for the linear time-varying system is deduced by employing the orthogonality relations and boundary values of shifted Legendre polynomials. Based on the model, the shifted Legendre polynomials coefficients of control function are iteratively adjusted by an optimal iterative learning law derived. The algorithm presented can avoid solving the state transfer matrix of linear time-varying systems. Simulation results illustrate the effectiveness of the proposed method.     

Study on the Application of Iterative Learning Control to Terminal Control of Linear Time-varying Systems

An iterative learning control algorithm based on shifted Legendre orthogonal polynomials is proposed to address the terminal control problem of linear time-varying systems. First, the method parameterizes a linear time-varying system by using shifted Legendre polynomials approximation. Then, an approximated model for the linear time-varying system is deduced by employing the orthogonality relations and boundary values of shifted Legendre polynomials. Based on the model, the shifted Legendre polynomials coefficients of control function are iteratively adjusted by an optimal iterative learning law derived. The algorithm presented can avoid solving the state transfer matrix of linear time-varying systems. Simulation results illustrate the effectiveness of the proposed method.     

Legendre orthogonal polynomials approximation of system gramians and its application to balanced truncation

The paper presents a procedure for computation of system gramians by using Legendre orthogonal polynomials approximation of the system state impulse and output responses. The proposed approach is trajectory based and relies on the system state and output trajectories snapshots selected either by experiment or computer simulation. It is defined in deterministic settings as opposed to similar approaches defined in stochastic settings by using the data covariance matrix. The advantage of using orthogonal series approximation for the gramians is to avoid solving the usual Lyapunov equations. The proposed method can be equally well applied to linear time-invariant as well as time-varying systems, and even to unstable systems, since the gramians approximation is performed on a finite interval of time. When the observation interval contains the whole energy of the system state impulse and output responses, the proposed method gives similar results as the gramians computed by solving Lyapunov equations. Several experiments are performed showing the good approximation properties of the presented method.     

多元Chebyshev正交多项式混合模型及其在医学图像分割中的应用

针对原有一元正交多项式混合模型只能根据灰度特征分割图像的问题,提出一种基于多元Chebyshev正交 多项式混合模型的多维特征的医学图像分割方法。首先,根据Fouricr分析方法与张量积理论推导出图像的多元 Chcbyshcv正交多项式,并构建多元正交多项式的非参数混合模型,用最小均方差(MISE)估计每一个模型的平滑参 数;然后,用EM算法求解正交多项式系数和模型的混合比。此方法不需要对模型作任何假设,可以有效克服“模型失 配”问题。通过实验,表明了该分割方法的有效性。     

Inverting non-minimum phase FIR transfer functions with application to reverberant speech

The problem of removing reverberation in speech is considered when the room impulse response is non-minimum phase. The method does not require multiple sensors or the use of all-pass transfer function networks as in previous techniques. Instead we use spectral factorization of large polynomials. Spectral factorization gives a method of reflecting the non-minimum phase roots without having to calculate their actual values.     

Identification of nonlinear systems via piecewise general orthogonal polynomials operator

Based on a hybrid orthogonal function, a new linear, continuous and bounded operator, piecewise general orthogonal polynomials operator (PGOPO), is proposed. Its main properties and operational rules have been strictly constructed based on the theory of convergence in the mean square, and are useful to discuss the orthogonal polynomial approach in the proper mathematics frame. Then applying the PGOPO method to solve the identification problem of nonlinear systems, the convergence analysis of PGOPO approximation method is given. Finally, using the PGOPO method to solve the parameter identification of two kinds of time-varying systems, the simulation studies show that the algorithm is simple and more effective than that of general orthogonal polynomials.     

Local representation of functions of D variables by means of discrete orthogonal polynomials

Discrete normalized orthogonal polynomials of D variables are defined by means of the orthogonal polynomials of a discrete variable introduced by Tchebychef. If a function of D variables is given by its values on a mesh, it may easily be expanded into a series of these polynomials of D variables. A truncation of this expansion is optimal in the sense of the method of least squares. The expansion may be used to study properties of the original function such a local extrema.     

基于脉冲响应的输出误差模型的辨识

基于系统脉冲响应参数, 利用相关分析方法, 提出了一种辨识输出误差模型参数的方法. 该方法是利用有限脉冲响应模型逼近输出误差模型, 通过依次递增脉冲响应参数的数目N来提高逼近精度. 理论分析表明, 只要N足够大, 模型的辨识精度可以满足实际要求. 提出的辨识方法可以在假设阶次N =1的条件下, 依次递增计算N较大时的脉冲响应参数和目标函数值, 从而根据脉冲响应确定系统的参数. 仿真试验说明提出的方法估计输出误差模型的参数是有效的.     

Linear system identification using numerical computation of Laplace transforms

A method for system identification using sampled values of the initial transient step or impulse response is described. A polynomial fit of the sampled values is made using Lagrange interpolation and the Laplace transform of the output observed is determined. Then the coefficients of the numerator and denominator polynomials of the system transfer function are determined by minimizing the square of the difference between the observed and calculated values of the Laplace transform of the output variable at a number of discrete points. This process is considerably simplified by the use of tables of coefficients for the numerical calculation of Laplace transforms.