动态系统的一阶特征模型与直线伺服系统的自适应迭代学习控制

就线性定常/时变系统以及非线性系统,依据特征模型理论,给出动态系统的一阶特征模型.其特征参数随时间变化,即以一阶时变差分方程描述受控系统的动态特性;与二阶和三阶特征模型相比较,一阶模型具更少参数.为解决由一阶特征模型描述的系统的控制问题,提出基于遗忘因子迭代学习辨识的自适应迭代学习控制方法.迭代学习辨识适于时变参数的估计,它允许被估计参数随时间快速变化,抑或突变.以直线伺服系统的位置跟踪控制为例,给出一种基于特征模型与LQ最优控制策略的自适应迭代学习控制方案.仿真与实验结果表明,提出的控制方案能够有效实现受控系统的位置跟踪控制.     

线性定常系统特征模型的特征参量辨识

说明线性定常系统特征模型的特征参量是一组由高阶线性定常系统的相关信息压缩而成,于是不能简单的作为与状态无关的慢时变参数来处理. 基于特征建模思想,建立了线性定常系统特征模型的特征参量与子空间方法之间的联系,给出了一种该特征模型的特征参量 的合成辨识算法.同时证明了在用于子空间辨识的样本量充分大和用于状态估计的时间充分长的情况下, 特征参量的估计值与真值之间的误差达到充分小. 最后,对于一个六阶的单输入单输出线性定常系统的仿真例子,对投影的带遗忘因子最小二乘算法和合成辨识算法进行了比较,验证了合成辨识算法的有效性.     

非线性时变系统特征建模与自适应迭代学习控制

讨论连续/离散非线性时变系统的特征建模,统一采用一阶时变差分方程作为特征模型.对于建模中可能产生的快变亦或突变的模型参数,以学习辨识方法进行估计;利用参数估值设计自适应迭代学习控制器,实现轨迹跟踪任务.参数估计学习算法包括带有遗忘因子的最小二乘学习算法和梯度学习算法.数值算例和电机位置跟踪实验结果表明所提出特征建模方法和学习控制方案的有效性.     

变时延过程的控制系统最小方差性能评价

针对单变量变时延过程中时延信息的估计问题和系统参数的辨识问题,分别研究了时延估计以及遗忘因子递推线性回归算法的最小方差性能基准.首先,利用系统过程运行数据,运用强跟踪滤波算法对时延信息进行估计,并根据时延改变情况将运行过程分段;然后,在每段时延固定的基础上,针对模型参数动态辨识,提出改进的遗忘因子递推线性回归算法的最小方差性能基准;最终,提出了变时延过程的最小方差性能基准的评价步骤.实验结果表明,相比较传统评价基准,变时延过程的最小反差性能评价基准的评价结果更加准确.     

具有时变灰参数的随机时滞系统的p-阶矩指数鲁棒稳定性

利用灰矩阵的矩阵覆盖集的分解技术和Lyapunov函数法,研究了具有时变灰色参数的随机时滞系统的p-阶矩指数鲁棒稳定性问题,得到了该系统p-阶矩指数鲁棒稳定的时滞独立和时滞依赖的条件,并通过数值例子说明了判别条件的有效性和实用性.     

一类时变大系统的区间矩阵平稳振荡

一类时变大系统的区间矩阵平稳振荡王美娟（上海机械学院基础部，上海２０００９３）在文献［１］中，我们讨论了具有分解的大系统的区间矩阵平稳振荡问题．其中Ａｓｓ为ｎｓ×ｎｓ阶实常量矩阵．平均法是用来解决时变系统问题的很有成效的一种方法．它使我们有可能从常数...     

时变高斯过程假设密度滤波算法

高斯过程是一种有效的数据驱动建模方法,已应用于解决时不变动态系统的状态估计问题.为了提升高斯过程动态系统的自适应能力,文章对参数时变的高斯过程动态系统,通过粒子滤波算法实时更新参数,将更新后的参数代入到高斯过程假设密度滤波算法得到时变高斯过程假设密度滤波算法.数值例子结果表明时变高斯过程假设密度算法的有效性.     

具有固定初始偏移的线性广义迭代学习控制系统的状态跟踪算法

本文研究线性广义系统存在固定初始偏移时的迭代学习控制问题.利用矩阵奇异值分解的方法,将广义系统转化为微分代数系统,再根据微分代数系统的性质,构建得到一种新的迭代学习控制算法,该算法由部分PD型算法和部分P型算法混合而成.利用压缩映射原理,证明在这种学习算法的作用下,系统的状态跟踪误差渐近收敛于零.为消除固定初始偏移的影响,本文进一步将初始修正策略应用到广义系统上,并由此构建得到相应的学习算法.证明在这种学习算法的作用下,可实现状态轨迹在预定有限时间区间上对期望轨迹的完全跟踪,且与初始偏移量的大小无关.仿真算例验证了算法的有效性.     

多参数结构特征二阶灵敏度

提出了一种有效计算多参数结构特征值与特征向量二阶灵敏度矩阵--Hessian矩阵的方法.将特征值和特征向量二阶摄动法转变为多参数形式,推导出二阶摄动灵敏度矩阵,由此得到特征值和特征向量的二阶估计式.该法解决了无法用直接求导法计算特征值和特征向量二阶灵敏度矩阵的问题.数值算例说明了该算法的应用和计算精度.     

用积分因子和特征值法求解常系数非齐次线性微分方程

提出一种求任意阶常系数非齐次线性微分方程通解的特征值分解联合积分因子的新方法.作为应用,联合Taylor展开可以解决一些偏微分方程径向解的问题.     

用改进遗传算法求解矩阵实特征值

依据矩阵特征值的分布理论,通过确定矩阵实特征值的分布区域,用实数编码和具有自适应交叉概率和变异概率的遗传算法来求解矩阵实特征值的近似值.仿真结果表明,此算法可以达到一定的精度,具有一定的通用性.并给求矩阵特征值提供了一种快速的方法.     

Stochastic gradient with changing forgetting factor-based parameter identification for Wiener systems

The parameter estimation problem is considered for a class Wiener systems. First, the effect of the forgetting factor on the stochastic gradient algorithm is analyzed. Then, a Wiener system stochastic gradient with a changing forgetting factor algorithm is presented which makes full use of the forgetting factor. Finally, an example is provided to test and verify the effectiveness of the proposed algorithms.     

On estimation of the optimal parameter of the modulus-based matrix splitting algorithm for linear complementarity problems on second-order cones

There are many studies on the well-known modulus-based matrix splitting (MMS) algorithm for solving complementarity problems, but very few studies on its optimal parameter, which is of theoretical and practical importance. Therefore and here, by introducing a novel mapping to explicitly cast the implicit fixed point equation and thus obtain the iteration matrix involved, we first present the estimation approach of the optimal parameter of each step of the MMS algorithm for solving linear complementarity problems on the direct product of second-order cones (SOCLCPs). It also works on single second-order cone and the non-negative orthant. On this basis, we further propose an iteration-independent optimal parameter selection strategy for practical usage. Finally, the practicability and effectiveness of the new proposal are verified by comparing with the experimental optimal parameter and the diagonal part of system matrix. In addition, with the optimal parameter, the effectiveness of the MMS algorithm can indeed be greatly improved, even better than the state-of-the-art solvers SCS and SuperSCS that solve the equivalent SOC programming.     

Complex-valued Zhang neural network for online complex-valued time-varying matrix inversion

In this paper, a new complex-valued recurrent neural network (CVRNN) called complex-valued Zhang neural network (CVZNN) is proposed and simulated to solve the complex-valued time-varying matrix-inversion problems. Such a CVZNN model is designed based on a matrix-valued error function in the complex domain, and utilizes the complex-valued first-order time-derivative information of the complex-valued time-varying matrix for online inversion. Superior to the conventional complex-valued gradient-based neural network (CVGNN) and its related methods, the state matrix of the resultant CVZNN model can globally exponentially converge to the theoretical inverse of the complex-valued time-varying matrix in an error-free manner. Moreover, by exploiting the design parameter γ>1, superior convergence can be achieved for the CVZNN model to solve such complex-valued time-varying matrix inversion problems, as compared with the situation without design parameter γ involved (i.e., the situation with γ=1). Computer-simulation results substantiate the theoretical analysis and further demonstrate the efficacy of such a CVZNN model for online complex-valued time-varying matrix inversion.     

A Fast Space-decomposition Scheme for Nonconvex Eigenvalue Optimization

In this paper, a nonsmooth bundle algorithm to minimize the maximum eigenvalue function of a nonconvex smooth function is presented. The bundle method uses an oracle to compute separately the function and subgradient information for a convex function, and the function and derivative values for the smooth mapping. Using this information, in each iteration, we replace the smooth inner mapping by its Taylor-series linearization around the current serious step. To solve the convex approximate eigenvalue problem with affine mapping faster, we adopt the second-order bundle method based on ????-decomposition theory. Through the backtracking test, we can make a better approximation for the objective function. Quadratic convergence of our special bundle method is given, under some additional assumptions. Then we apply our method to some particular instance of nonconvex eigenvalue optimization, specifically: bilinear matrix inequality problems.     

Recursive computational formulas of the least squares criterion functions for scalar system identification

The paper discusses recursive computation problems of the criterion functions of several least squares type parameter estimation methods for linear regression models, including the well-known recursive least squares (RLS) algorithm, the weighted RLS algorithm, the forgetting factor RLS algorithm and the finite-data-window RLS algorithm without or with a forgetting factor. The recursive computation formulas of the criterion functions are derived by using the recursive parameter estimation equations. The proposed recursive computation formulas can be extended to the estimation algorithms of the pseudo-linear regression models for equation error systems and output error systems. Finally, the simulation example is provided.     

An iterative least squares estimation algorithm for controlled moving average systems based on matrix decomposition

An iterative least squares parameter estimation algorithm is developed for controlled moving average systems based on matrix decomposition. The proposed algorithm avoids repeatedly computing the inverse of the data product moment matrix with large sizes at each iteration and has a high computational efficiency. A numerical example indicates that the proposed algorithm is effective.     

The calculation of the distance to a nearby defective matrix

The distance of a matrix to a nearby defective matrix is an important classical problem in numerical linear algebra, as it determines how sensitive or ill‐conditioned an eigenvalue decomposition of a matrix is. The concept has been discussed throughout the history of numerical linear algebra, and the problem of computing the nearest defective matrix first appeared in Wilkinsons famous book on the algebraic eigenvalue problem. In this paper, a new fast algorithm for the computation of the distance of a matrix to a nearby defective matrix is presented. The problem is formulated following Alam and Bora introduced in (2005) and reduces to finding when a parameter‐dependent matrix is singular subject to a constraint. The solution is achieved by an extension of the implicit determinant method introduced by Spence and Poulton in (2005). Numerical results for several examples illustrate the performance of the algorithm. Copyright © 2013 John Wiley & Sons, Ltd.     

A fast algorithm for computing the smallest eigenvalue of a symmetric positive‐definite Toeplitz matrix

Recent progress in signal processing and estimation has generated considerable interest in the problem of computing the smallest eigenvalue of a symmetric positive‐definite (SPD) Toeplitz matrix. An algorithm for computing upper and lower bounds to the smallest eigenvalue of a SPD Toeplitz matrix has been recently derived (Linear Algebra Appl. 2007; DOI: 10.1016/j.laa.2007.05.008 ). The algorithm relies on the computation of the R factor of the QR factorization of the Toeplitz matrix and the inverse of R. The simultaneous computation of R and R^?1 is efficiently accomplished by the generalized Schur algorithm. In this paper, exploiting the properties of the latter algorithm, a numerical method to compute the smallest eigenvalue and the corresponding eigenvector of SPD Toeplitz matrices in an accurate way is proposed. Copyright © 2008 John Wiley & Sons, Ltd.     

Parameter and state estimation algorithm for single-input single-output linear systems using the canonical state space models

This paper presents a new parameter and state estimation algorithm for single-input single-output systems based on canonical state space models from the given input–output data. Difficulties of identification for state space models lie in that there exist unknown noise terms in the formation vector and unknown state variables. By means of the hierarchical identification principle, those noise terms in the information vector are replaced with the estimated residuals and a new least squares algorithm is proposed for parameter estimation and the system states are computed by using the estimated parameters. Finally, an example is provided.