On positive real transfer functions and the convergence of some recursive schemes

The convergence with probability one of a recently suggested recursive identification method by Landau is investigated. The positive realness of a certain transfer function is shown to play a crucial role, both for the proof of convergence and for convergence itself. A completely analogous analysis can be performed also for the extended least squares method and for the self-tuning regulator of Åström and Wittenmark. Explicit conditions for convergence of all these schemes are given. A more general structure is also discussed, as well as relations to other recursive algorithms.     

多变量系统的耦合梯度辨识算法与性能分析

针对多变量系统维数大、参数多、一般的辨识算法计算量大的问题, 基于耦合辨识概念, 推导多变量系统的耦合随机梯度算法, 利用鞅收敛定理分析算法的收敛性能. 算法的主要思想是将系统模型分解为多个单输出子系统,在子系统的递推辨识过程中, 将每个子系统的参数估计值耦合起来. 所提出算法与最小二乘算法和耦合最小二乘算法相比, 具有较少的计算量, 收敛速度可以通过引入遗忘因子得到改善. 性能分析表明了所提出算法收敛, 仿真实例验证了算法的有效性.

     

一种不完全信息下递推辨识方法及收敛性分析

针对信号在网络环境下传输带来不完全信息使得在线参数辨识算法和收敛性困难的问题, 不同于传统递推最小二乘方法, 本文提出了一种不完全信息下递推辨识方法并分析其收敛性. 首先运用伯努利分布刻画引起不完全信息的数据丢包特性, 然后基于辅助模型方法补偿不完全信息并构造了新的数据信息矩阵, 并运用矩阵正交变换性质对数据信息矩阵进行QR分解, 推导了融合网络参数的递推辨识新算法, 理论证明了在不完全信息下递推参数辨识算法的收敛性. 最后仿真结果验证了所提方法的可行性和有效性.     

On-line identification of a heat exchanger with a process computer—A case study

For on-line identification and parameter estimation of industrial processes with process computers an identification program package was developed. Three appropriate identification methods can be selected: recursive least squares, recursive instrumental variables and recursive correlation analysis with least squares. The program package also includes: signal generation, determination of model order and time delay, data filtering for the elimination of low frequent disturbances, model verification and plotting of intermediate and final results. Practical results and comparisons with the identification package are shown for an industrial size steam-heated heat exchanger.     

多变量线性系统结构和参数辨识的递推最小二乘法

本文研究多变量线性系统的结构和参数辨识.利用解不定对称系数方程组的方法,导出了搜索系统结构特征值的最小二乘递推算法.并提出了一个判断系统结构的新准则——系统特征方程系数符号检验法.把两者结合在一起,构成了完整的多变量系统结构和参数辨识的递推最小二乘法,并给出了仿真例子. 本方法也可作为最小二乘的各种改进算法(如广义最小二乘法等)的基础.     

Box-Jenkins模型偏差补偿方法与其他辨识方法的比较

对于存在相关噪声干扰的Box—Jenkins系统,本文借助于偏差补偿原理,推导了一个偏差补偿最小二乘(BCLS)辨识方法;理论分析说明BCLS方法能够给出系统模型参数的无偏估计,并将提出的方法与递推增广最小二乘算法和递推广义增广最小二乘算法进行了比较研究;用仿真试验分析了这些算法的各自特点和适用范围。     

An efficient hierarchical identification method for general dual-rate sampled-data systems

For the lifted input–output representation of general dual-rate sampled-data systems, this paper presents a decomposition based recursive least squares (D-LS) identification algorithm using the hierarchical identification principle. Compared with the recursive least squares (RLS) algorithm, the proposed D-LS algorithm does not require computing the covariance matrices with large sizes and matrix inverses in each recursion step, and thus has a higher computational efficiency than the RLS algorithm. The performance analysis of the D-LS algorithm indicates that the parameter estimates can converge to their true values. A simulation example is given to confirm the convergence results.     

基于KRLS的非均匀采样非线性系统辨识

利用提升技术可将非均匀采样非线性系统离散化为一个多输入单输出传递函数模型,从而将系统输出表示为非均匀刷新非线性输入和输出回归项的线性参数模型,进一步基于非线性输入的估计或过参数化方法进行辨识.然而,当非线性环节结构未知或不能被可测非均匀输入参数化表示时,上述辨识方法将不再适用.为了解决这个问题,利用核方法将原始非线性数据投影到高维特征空间中使其线性可分,再对投影后的数据应用递推最小二乘算法进行辨识,提出基于核递推最小二乘的非均匀采样非线性系统辨识方法.此外,针对系统含有有色噪声干扰的情况,参考递推增广最小二乘算法的思想,利用估计残差代替不可测噪声,提出核递推增广最小二乘算法.最后,通过仿真例子验证所提算法的有效性.     

差分模型参数递推估计的Householder变换法

本文提出了利用Householder变换进行差分模型参数递推估计的新方法.并由该方法导 出了新的递推最小二乘法、递推增广矩阵法、递推广义最小二乘法、递推极大似然法. 文中分单变量、多变量两种情况重点讨论了新递推最小二乘法及其与传统递推最小二乘 法的比较,并给出了计算实例.     

Recursive identification method for MISO Wiener-Hammerstein model

A simple technique for recursive identification of the Wiener-Hammerstein model with extension to the multi-input single-output (MISO) case is presented. We use a new transformation of the input-output difference equation where parameters to be estimated are those of each subsystem of the initial and unique realization. After that, a weighted extended least squares method is employed to estimate recursively and separately parameters of the linear subsystems and the static nonlinear element. The convergence analysis of the proposed procedure is also studied. Finally, a numerical example is provided to show the efficiency of the algorithm     

Transfer function synthesis using frequency response data

Various linear least squares methods for transfer function synthesis from frequency response data are presented in a unified format. Solutions are derived from Householder transformations and recursive least squares. An alternative formulation derived from a time domain error criterion is also shown to be of the linear least squares type. The comparative performance of the various methods is illustrated by several examples.     

Adaptive recursive algorithm with logarithmic transformation for nonlinear system identification in α-stable noise

Although the least mean pth power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filters outperform the conventional least mean square (LMS) algorithm in the presence of α-stable noise, they still exhibit slow convergence and high steady-state kernel error in nonlinear system identification. To overcome these limitations, an enhanced recursive least mean pth power algorithm with logarithmic transformation (RLogLMP) is proposed in this paper. The proposed algorithm is adjusted to minimize the new cost function with the p-norm logarithmic transformation of the error signal. The logarithmic transformation, which can diminish the significance of outliers under α-stable noise environment, increases the robustness of the proposed algorithm and reduces the steady-state kernel error. Moreover, the proposed method improves the convergence rate by the enhanced recursive scheme. Finally, simulation results demonstrate that the proposed algorithm is superior to the LMP, NLMP, normalized least mean absolute deviation (NLMAD), recursive least squares (RLS) and nonlinear iteratively reweighted least squares (NIRLS) algorithms in terms of convergence rate and steady-state kernel error.     

Implicit predictive adaptive control with stochastic gradientidentifiers

The replacement in an implicit predictive adaptive controller of recursive least squares (RLS) identifiers with stochastic gradient (SG) identifiers is considered. By an ordinary differential equation analysis, local convergence properties of the new algorithm are investigated. The conclusions, supported by simulation results, are that, in contrast with the one-step-ahead self-tuning regulator, the convergence properties of the resulting adaptive controller deteriorate if RLS identifiers are replaced with SG identifiers     

Analysis of stochastic approximation schemes with discontinuous and dependent forcing terms with applications to data communication algorithms

A general convergence result is given for stochastic approximation schemes with (or without) equality constraints. The following features are taken into account. The forcing term is a strongly dependent sequence and may be discontinuous. Many examples are given to illustrate the applicability of the convergence theorem, both classical (recursive least squares scheme) and nonclassical ones (arising in the theory of self-adaptive eqnalizers).     

Principal component extraction using recursive least squareslearning

A new neural network-based approach is introduced for recursive computation of the principal components of a stationary vector stochastic process. The neurons of a single-layer network are sequentially trained using a recursive least squares squares (RLS) type algorithm to extract the principal components of the input process. The optimality criterion is based on retaining the maximum information contained in the input sequence so as to be able to reconstruct the network inputs from the corresponding outputs with minimum mean squared error. The proof of the convergence of the weight vectors to the principal eigenvectors is also established. A simulation example is given to show the accuracy and speed advantages of this algorithm in comparison with the existing methods. Finally, the application of this learning algorithm to image data reduction and filtering of images degraded by additive and/or multiplicative noise is considered.     

基于免疫RBF神经网络的逆运动学求解

求解机械臂逆运动学问题可以采用神经网络来建立逆运动学模型,通过遗传算法或BP算法训练神经网络的权值从而得到问题的解,在求解精度和收敛速度上有待进一步改进。采用人工免疫原理对RBF网络训练数据集的泛化能力在线调整隐层结构,生成RBF网络隐层。当网络结构确定时,采用递推最小二乘法确定网络连接权值。由此对神经网络的网络结构和连接权进行自适应调整和学习。通过仿真可以看出,用免疫原理训练的神经网络收敛速度快,泛化能力强,可大幅提高机械臂逆运动学求解精度。     

Parametric estimation of interconnected nonlinear systems described by input-output mathematical models

In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems,which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.     

Recursive identification for multi-input–multi-output Hammerstein–Wiener system

In this paper, an identification method based on the recursive auxiliary variable least squares algorithm is proposed for a multi-input–multi-output Hammerstein–Wiener system with process noise. In the proposed identification method, the system is converted into the multivariate regression form under the condition that the nonlinear block in the output part is invertible. Then, the auxiliary variable is constructed, the parameters of the regression equations are identified, and the system parameter matrices can be obtained by matrix composition of the parameter product matrix. A theoretical analysis showed that the proposed method has uniform convergence when the process noise is white and has a finite variance. The effectiveness of the proposed method is validated through the experiments.