态空间系统的梯度优化辨识及收敛性分析*

为解决状态空间系统的预报误差与系统参数之间的非线性、非凸性给参数估计带来的困难,提出了状态空间系统的梯度优化辨识方法。分析了基于局部线性化的梯度辨识原理,给出了基于QR分解、奇异值分解(SVD)确定参数搜索方向的实现方案,得到了估计系统参数的迭代辨识算法。探讨了算法的收敛性、给出了算法收敛速度的解析表达式,最后进行了数值仿真,实验结果说明了所提出方法的有效性。     

Eigenvalue convergence properties of spatially discretised partial differential equations

A theorem is presented along with proof for the convergence properties of eigenvalues of differential-difference equations corresponding to spatially discretized partial differential-equations describing lateral vibration of bars. Eigenvalues obtained from analytical solutions of partial differential equations confirm the proof.     

Solving certain queueing problems modelled by toeplitz matrices

By using the concept of generating function associated with a Toeplitz matrix, we analyze existence conditions for the probability invariant vector π of certain stochastic semi-infinite Toeplitz-like matrices. An application to the shortest queue problem is shown. By exploiting the functional formulation given in terms of generating functions, we devise a weakly numerically stable algorithm for computing the probability invariant vector π. The algorithm is divided into three stages. At the first stage the zeros of a complex function are numerically computed by means of an extension of the Aberth method. At the second stage the first k components of π are computed by solving an interpolation problem, where k is a suitable constant associated with the matrix. Finally, at the third stage a triangular Toeplitz system is solved and its solution is refined by applying the power method or any other refinement method based on regular splittings. In the solution of the triangular Toeplitz system and at each step of the refinement method, special FFT-based techniques are applied in order to keep the arithmetic cost within the O(n log n) bound, where n is an upper bound to the number of the computed components. Numerical comparisons with the available algorithms show the effectiveness of our algorithm in a wide set of cases.     

求解无约束优化问题的知识进化算法及其收敛性分析

针对传统方法的随机盲目性和易陷入局部最优值等缺陷,提出一种求解无约束优化问题的知识进化算法(简称为UOP-KEA),并对算法的全局收敛性进行了分析.该算法的主要思想是:首先建立初始知识库,然后利用传承算子来实现对优秀知识个体的传承,利用创新算子来产生新的知识个体,利用更新算子来更新知识库,从而实现知识的进化,最后从知识库的最优知识个体中获取问题的最优解.将该算法应用于无约束非线性测试函数的最小值优化求解,获得了成功的结果.与遗传算法相比,该算法可以使用较小的种群规模,以较快的速度寻找到全局最优解,表明了它的可行性和有效性.     

VCP拥塞控制协议公平性收敛的动态分析

VCP协议是一种新型的、易于实现的拥塞控制协议,适用于高带宽时延乘积网络的拥塞控制。系统地分析了VCP协议公平性收敛的动态问题,包括公平性收敛的动态模型的建立、公平性收敛的动态分析等。动态分析为VCP协议中一些参数的选择提供了新的依据。     

FKA算法迭代收敛性分析

《核选择和非线性特征提取的双线性分析》一文提出了一种新颖的核Fisher准则FKC, 并用迭代分析算法FKA求得最优解,但其迭代收敛性缺乏理论上的证明。从理论上对FKA算法的迭代收敛性进行了分析和探讨,并运用Radermacher复杂性分析法进行证明。     

PSO算法的收敛性及参数选择研究

PSO算法(微粒群算法)是一种仿生优化技术,目前国内外对该算法的研究成果已经很丰富。然而PSO的数学基础还显得相对薄弱,对该算法的研究也仅仅限于在一维问题域内的收敛情况,对二维以及多维算法域收敛稳定性还缺乏深刻且具有普遍意义的理论分析。因此,在介绍分析一维问题域算法收敛的基础上,研究PSO算法在二维以及多维算法域内的收敛情况,从而寻求更加有利于微粒群算法收敛的参数选择。     

改进蚁群算法在应急VRP中的应用及收敛性分析

应急条件(地震、泥石流、洪水等)下的路况不稳定,随时会发生意外的问题.为了解决应急条件下的物资分配,在研究蚁群算法解决传统VRP(vehicle routing problem)的基础上,通过加入动态路况子对VRP数学模型进行改进,提出蚁群算法对改进后的车辆路路径问题的数学模型,并利用陕西省21个城市的实际经纬度作为应急情况下的模拟货物需求地点和仓库进行系统仿真,对影响改进算法收敛性的参数进行分析.通过理论研究和MATLAB仿真,证明了这种改进的算法能够有效解决实际情况中的应急物流分配问题.     

Some global and local convergence analysis on the information-theoretic independent component analysis approach

In this paper, we present a detailed theoretical analysis on the information-theoretic Independent Component Analysis (IT-ICA) approach. We first provide a number of lemmas and theorems on properties of the corresponding cost function in the general n-channel case with differentiable, odd, monotonic decreasing nonlinearity. A theorem on behaviour of the cost function along a radially outward line is given for characterizing the global configuration of the cost function in the parameter space. Furthermore, on the 2-channel IT-ICA system with cubic nonlinearity, we not only exhaustively solve out all equilibrium points and the condition for stability, but also give a global convergence theorem.     

改进遗传算法全局收敛性分析

传统的遗传算法大多数没有给出收敛性准则。一类新的改进的遗传算法被提出,该算法即考虑了优化问题的全局性要求——每一步构造一个新函数,而这往往却比局部最优理论和方法困难得多;同时通过对选择算子的改进,对遗传算法后期进化缓慢问题得到了有效控制,最后给出了算法的收敛性证明以及收敛性准则。实例证明该算法是有效的。     

Recursive identification under scarce measurements — convergence analysis

In this paper, the problem of recursive identification under scarce-data operation is addressed. The control action is assumed to be updated at a fixed rate, while the output is assumed to be measured synchronously with the input update, but with an irregular availability pattern. Under these conditions the use of pseudo-linear recursive algorithms is studied. The main result is the convergence analysis for the case of regular but scarce data availability. The existence of wrong attractors is demonstrated, and a local stability condition of the identification algorithm is derived.     

交替捕食的粒子群优化算法及其粒子轨迹收敛性分析

为避免算法陷入局部极值,在捕食者一猎物协同进化机制基础上,提出了一种交替捕食的粒子群优化算法(APPSO).对该算法迭代过程进行了分析,给出并证明了粒子运动轨迹收敛的充分条件.为使粒子运动轨迹可靠收敛,构建了一种参数设置方法.通过迭代矩阵谱半径计算、SQRT序列采样,对该算法的粒子轨迹收敛速度进行了分析.基准测试函数仿真结果表明,交替捕食的PSO算法具有较佳的搜索性能.     

The modes of convergence in the approximation of fuzzy random optimization problems

To develop the approximation approach to fuzzy random optimization problems, it is required to introduce the modes of convergence in fuzzy random theory. For this purpose, this paper first presents several novel convergence concepts for sequences of fuzzy random variables, such as convergence in chance, convergence in distribution and convergence in optimistic value; then deals with the convergence criteria and convergence relations among various types of convergence. Finally, we deal with the convergence theorems for sequences of integrable fuzzy random variables, including dominated convergence theorem and bounded convergence theorem.     

Several NP-hard problems arising in robust stability analysis

We demonstrate that it is NP-hard to check whether all representatives of a square interval matrix share any of the following four properties: positive semidefiniteness, provided that the matrix is symmetric; norm 1; nonsingularity (NP-hardness of this particular problem was established recently by Poljak and Rohn); or stability (all eigenvalues in the open left half-plane).This work was completed while on leave at INRIA-Rocquencourt, Domaine de Voluceau, Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France.     

用割线法迭代求解对称三对角矩阵特征值问题

为对称三对角矩阵特征值问题，提出一种新的分而治之的算法。新算法以二分法，割线法迭代为基础，不同于Ｃｕｐｐｅｎ的方法和Ｌａｎｇｕｅｒｒｅ迭代法。理论分析和数据实验的结果表明：新算法的收敛速度明显比文［１］中的Ｌａｇｕｅｒｒｅ迭代法快。     

A study on the convergence of observer-based kinetics estimators in stirred tank bioreactors

This paper is devoted to the tuning problem of an observer-based algorithm for the on-line estimation of reaction rates in stirred tank bioreactors. The relation between the dynamics of convergence and the tuning procedure is explored. The method proposed imposes a variable second-order dynamics on the convergence of the estimator. This approach is shown to compare favourably with a pole placement based technique, in an application to a baker's yeast fed-batch fermentation.     

On exponential convergence and robustness of least-squares identification

Robustness and convergence properties of exponentially weighted least-squares identification are studied. It is shown that exponential convergence in the noiseless case can be obtained for a class of increasing or decreasing regression vectors. The rate of change of the limits in the regressors affect the convergence rates, which are explicitly given. It is demonstrated that for a sub-class of regressors decreasing-in-the-norm exponential convergence without the noise does not guarantee robustness subject to a bounded noise. Instead, exponential divergence of the estimate is shown in a specific case.     

自校正多传感器观测融合Kalman估值器及其收敛性分析

对于带未知噪声方差的多传感器系统,应用加权最小二乘(WLS)法得到了一个加权融合观测方程,且它与状态方程构成一个等价的观测融合系统.应用现代时间序列分析方法,基于观测融合系统的滑动平均(MA)新息模型参数的在线辨识,可在线估计未知噪声方差,进而提出了一种加权观测融合自校正Kalman估值器,可统一处理自校正融合滤波、预报和平滑问题,并用动态误差系统分析方法证明了它的收敛性,即若MA新息模型参数估计是一致的,则它按实现或按概率1收敛到全局最优加权观测融合Kalman估值器,因而具有渐近全局最优性.一个带3传感器跟踪系统的仿真例子说明了其有效性.