模糊相轨迹模型Smith预估控制

针对一类可重复运行的时滞过程,将Smith预估控制的结构进行变形,以系统输出的相轨迹作为预估模型.证明指出只要原系统闭环稳定则相轨迹模型Smith预估控制系统稳定,且给出了算法的收敛性判据.为了得到相轨迹模型,用模糊方法对系统输出进行逼近,同时辨识了纯滞后时间.仿真表明,所提方法不需要已知过程的模型.通过一定次数的"迭代"即可克服纯滞后,从而克服了常规算法控制品质依赖精确数学模型的缺陷.同时该算法具有较强的鲁棒性.     

内部输入带不同时滞的Timoshenko梁的指数稳定性

研究了内部输入带不同时滞的Timoshenko梁的指数稳定性.利用Smith预估器的思想,对部分状态进行预估可得无时滞系统.对无时滞系统设计控制器,得到闭环系统.通过讨论闭环系统的稳定性及原时滞系统和无时滞系统的误差系统的指数衰减,最终得出原系统的指数稳定性.     

三级倒立摆的T-S型前馈补偿模糊神经网络控制

为解决T akag i-Sugeno型模糊神经网络在控制多变量系统时的规则组合爆炸问题,提出一种误差前馈补偿的模糊神经网络控制方案,有效实现了三级倒立摆的稳定控制。该控制方案适用对状态变量可按性质和重要程度划分的多变量系统的控制,大大减少了模糊神经网络控制器的规则数,有利于利用专家的控制经验,具有良好的鲁棒性和非线性适应能力。     

非线性多时滞系统的直接自适应模糊控制

针对一类单输入单输出非线性多时滞系统,提出了一种自适应模糊跟踪控制方案.该方案结合了自适应控制和H∞控制.构建了自适应时滞模糊逻辑系统用来逼近未知时滞函数;设计了H∞补偿器来抵消模糊逼近误差和外部扰动.根据跟踪误差给出了参数调节规律.证明了误差闭环系统满足期望的H∞跟踪性能.仿真结果表明了该方案的有效性.     

基于模糊与神经网络技术的复杂非线性跟踪控制

针对一类具有不确定性、多重时延和状态未知的复杂非线性系统,把模糊T-S模型和RBF神经网络结合起来,提出了一种基于观测器的跟踪控制方案.首先,应用模糊T-S模型对非线性系统建模,设计观测器用来观测系统状态,并由线性矩阵不等式得到模糊模型的控制律;其次,构建了自适应RBF神经网络,应用自适应RBF神经网络作为补偿器来补偿建模误差和不确定非线性部分.证明了闭环系统满足期望的跟踪性能.示例仿真结果表明了该方案的有效性.     

不确定对象的自学习模糊神经网络控制方法

本文对具有不确定性控制对象提出了一种自学习模糊神经网络控制方法，模糊控制器采用误差，误差变化及误差加速度的加权和解析描述形式，利用人工神经网络直接对过程的建模，实现对模糊加权因子的自学习优化调整。将上述方法用于焊接熔池动态过程控制实实验，结果表明本文提出的自学习模糊神经网络控制方案有效。     

基于有序梯形模糊灰色关联TOPSIS的多属性决策方法

研究了有序梯形模糊数来表示不确定语言环境下的灰色关联TOPSIS多属性决策问题。首先应用有序梯形模糊数标度方案属性偏好信息,在传统梯形模糊数基础上增加了一个方向属性,使得决策信息的表示更加细腻;提出了有序梯形模糊环境下多属性决策灰色关联TOPSIS综合优选算法,引入了距离和灰色关联度相结合的综合贴近度公式,实现最优方案与理想方案的位置与曲线形状的一致性;最后通过制造系统内流动控制实例说明了所提出有序梯形模糊灰色关联TOPSIS方法的可行性和有效性。     

Willis环状脑动脉瘤系统的自适应模糊控制

针对不确定非线性生物系统—W illis环状脑动脉瘤系统,利用高斯型模糊逻辑系统的逼近能力及新构造的Lyapunov函数,基于模糊建模提出了一种自适应模糊控制器设计的新方案.该方案把逼近误差引入到控制器设计条件中用以改善系统的动态性能.不但设计简单还保证了控制方法的鲁棒性与稳定性.通过反向传播算法调整模糊基函数参数及递归最小二乘法调整参数向量,θ更新控制律,实现了理想跟踪.从理论上研究了脑动脉瘤内血流速度的非线性行为及控制,具有实际意义.仿真结果表明该控制方法的有效性.     

多输入多输出非线性最小相位系统的自适应模糊控制

针对多输入多输出非线性最小相位系统,把自适应模糊控制和自适应模糊辨识结合起来,提出了一种自适应模糊控制方案.设计辨识器用来辨识系统的未知部分;然后由跟踪误差和辨识误差给出了参数调节规律,两种误差同时调节参数改善了系统性能.模糊逻辑系统用来估计未知函数.控制方案保证了系统的稳定性,实现了有界跟踪.仿真结果表明了该方案的可行性.     

基于区间直觉犹豫模糊集VIKOR扩展方法的突发公共事件处置方案决策模型

处理突发公共事件时,要对应急处里方案进行评估决策,其本质是一个多准则群决策问题,专家组在决策过程中存在一定犹豫度。本文提出应急处置方案评估标准体系,在区间直觉犹豫模糊理论基础上建立应急处置方案评估模型。通过最大化团队自信程度确定专家权重,提出调整型区间直觉犹豫模糊加权平均算子集成决策者意见,基于VIKOR扩展方法对应急处置方案进行排序,并通过算例验证模型的可行性和有效性。该模型在整个应急处置方案决策过程中始终保证决策信息为区间直觉犹豫模糊元,既控制了计算和表达复杂度,又避免了群体决策信息流失。     

A new version of the Smith method for solving Sylvester equation and discrete-time Sylvester equation

Recently, Xue etc. \cite{28} discussed the Smith method for solving Sylvester equation $AX+XB=C$, where one of the matrices $A$ and $B$ is at least a nonsingular $M$-matrix and the other is an (singular or nonsingular) $M$-matrix. Furthermore, in order to find the minimal non-negative solution of a certain class of non-symmetric algebraic Riccati equations, Gao and Bai \cite{gao-2010} considered a doubling iteration scheme to inexactly solve the Sylvester equations. This paper discusses the iterative error of the standard Smith method used in \cite{gao-2010} and presents the prior estimations of the accurate solution $X$ for the Sylvester equation. Furthermore, we give a new version of the Smith method for solving discrete-time Sylvester equation or Stein equation $AXB+X=C$, while the new version of the Smith method can also be used to solve Sylvester equation $AX+XB=C$, where both $A$ and $B$ are positive definite. % matrices. We also study the convergence rate of the new Smith method. At last, numerical examples are given to illustrate the effectiveness of our methods     

A Modified Low-Rank Smith Method for Large-Scale Lyapunov Equations

In this note we present a modified cyclic low-rank Smith method to compute low-rank approximations to solutions of Lyapunov equations arising from large-scale dynamical systems. Unlike the original cyclic low-rank Smith method introduced by Penzl in [20], the number of columns required by the modified method in the approximate solution does not necessarily increase at each step and is usually much lower than in the original cyclic low-rank Smith method. The modified method never requires more columns than the original one. Upper bounds are established for the errors of the low-rank approximate solutions and also for the errors in the resulting approximate Hankel singular values. Numerical results are given to verify the efficiency and accuracy of the new algorithm.     

A low-rank Krylov squared Smith method for large-scale discrete-time Lyapunov equations

The squared Smith method is adapted to solve large-scale discrete-time Lyapunov matrix equations. The adaptation uses a Krylov subspace to generate the squared Smith iteration in a low-rank form. A restarting mechanism is employed to cope with the increase of memory storage of the Krylov basis. Theoretical aspects of the algorithm are presented. Several numerical illustrations are reported.     

Issues with the Smith–Wilson method

We analyse various features of the Smith–Wilson method used for discounting under the EU regulation Solvency II, with special attention to hedging. In particular, we show that all key rate duration hedges of liabilities beyond the Last Liquid Point will be peculiar. Moreover, we show that there is a connection between the occurrence of negative discount factors and singularities in the convergence criterion used to calibrate the model. The main tool used for analysing hedges is a novel stochastic representation of the Smith–Wilson method.     

On the squared Smith method for large‐scale Stein equations

A squared Smith type algorithm for solving large‐scale discrete‐time Stein equations is developed. The algorithm uses restarted Krylov spaces to compute approximations of the squared Smith iterations in low‐rank factored form. Fast convergence results when very few iterations of the alternating direction implicit method are applied to the Stein equation beforehand. The convergence of the algorithm is discussed and its performance is demonstrated by several test examples. Copyright © 2013 John Wiley & Sons, Ltd.     

Convergence acceleration of alternating series

Numerical Algorithms - We propose a new simple convergence acceleration method for a wide range class of convergent alternating series. It has some common features with Smith’s and...     

Smith meets Smith: Smith normal form of Smith matrix

In 1861, Henry John Stephen Smith [H.J.S. Smith, On systems of linear indeterminate equations and congruences, Philos. Trans. Royal Soc. London. 151 (1861), pp. 293–326] published famous results concerning solving systems of linear equations. The research on Smith normal form and its applications started and continues. In 1876, Smith [H.J.S. Smith, On the value of a certain arithmetical determinant, Proc. London Math. Soc. 7 (1875/76), pp. 208–212] calculated the determinant of the n?×?n matrix ((i,?j)), having the greatest common divisor (GCD) of i and j as its ij entry. Since that, many results concerning the determinants and related topics of GCD matrices, LCM matrices, meet matrices and join matrices have been published in the literature. In this article these two important research branches developed by Smith, in 1861 and in 1876, meet for the first time. The main purpose of this article is to determine the Smith normal form of the Smith matrix ((i,?j)). We do this: we determine the Smith normal form of GCD matrices defined on factor closed sets.     

节点失效下全端可靠性的上界

推广了A bdu llah K onak and A lice E.Sm ith提出的方法,在链路和节点均不可靠的条件下,给出了全端可靠性上界的估算公式,利用该公式估算上界简洁方便,精度高.具有实用价值.     

Diophantine Quadratic Equation and Smith Normal Form Using Scaled Extended Integer Abaffy–Broyden–Spedicato Algorithms

Classes of integer Abaffy–Broyden–Spedicato (ABS) methods have recently been introduced for solving linear systems of Diophantine equations. Each method provides the general integer solution of the system by computing an integer solution and an integer matrix, named Abaffian, with rows generating the integer null space of the coefficient matrix. The Smith normal form of a general rectangular integer matrix is a diagonal matrix, obtained by elementary nonsingular (unimodular) operations. Here, we present a class of algorithms for computing the Smith normal form of an integer matrix. In doing this, we propose new ideas to develop a new class of extended integer ABS algorithms generating an integer basis for the integer null space of the matrix. For the Smith normal form, having the need to solve the quadratic Diophantine equation, we present two algorithms for solving such equations. The first algorithm makes use of a special integer basis for the row space of the matrix, and the second one, with the intention of controlling the growth of intermediate results and making use of our given conjecture, is based on a recently proposed integer ABS algorithm. Finally, we report some numerical results on randomly generated test problems showing a better performance of the second algorithm in controlling the size of the solution. We also report the results obtained by our proposed algorithm on the Smith normal form and compare them with the ones obtained using Maple, observing a more balanced distribution of the intermediate components obtained by our algorithm.