SISO系统的鲁棒性能设计

本文讨论了ＳＩＳＯ系统的鲁棒性能设计问题。根据具有乘性不确定性ＳＩＳＯ系统鲁棒性能指标μ的显式表达式,分析了μ综合中权函数的选择,文中还配有例题进行说明。     

方块脉冲函数用于连续分布时滞系统的最优控制

本文应用方块脉冲函数推出了连续分布时滞系统的分段恒定解答,给出了最优控制的综合表达式及泛函目标的最优值。     

病态对象的鲁棒性能设计*

病态对象因为其高条件数的特点为系统的鲁棒性能设计带来困难，μ综合中Ｍ阵具有四块结构，适于求解这类病态问题，而且结构奇异值μ是鲁棒性能的充要判据。本文给出Ｄ－Ｋ迭代中初值Ｄ０阵的选取方法，可以较快地求得μ综合解，文中还以精馏塔鲁棒控制设计为例进行了说明。     

分层云不确定推理系统及其逼近性能分析

为了解决目前基于云模型的智能控制和预测中规则数目随系统变量的个数呈指数增长的问题,设计分层云不确定性推理系统,并证明该系统的逼近性能。采用基于云理论的新的不确定性推理模型来设计分层云不确定性推理系统并给出解析表达式。证明分层云不确定性推理系统对致密集上函数的逼近能力。结果表明：分层云不确定性推理系统的输出结果计算式满足Stone-Weirstrass定理的3个假设条件,具有万能逼近性质。     

关于结构奇异值的一个注记

１引言Ｄｏｙｌｅ在１９８２年提出的结构奇异值（μ）方法是分析和综合结构式不确定系统的有力工具［１，２］．基于结构奇异值分析的小μ定理［２］给出了具有多个摄动块的线性动态系统鲁棒稳定的充要条件．而鲁棒性能定理［２］则进一步地将鲁棒稳定性问题和鲁棒性能问题统一成μ分析问题．然而．我们注意到，在所有研究结构奇异值的文献中，均要求块对角摄动矩阵中每个子摄动块是方的．这一要求无疑大大限制了μ方法的应用，因为非方摄动块在系统中是经常存在的．此时对Ｄｏｙｌｅ给出的结构奇异值的上界函数［１］必须进行修正．２非方…     

XML的函数依赖

通过分析函数依赖的表现形式在XML文档和关系数据库中的不同之处，提出了基于DTD中的路径表达式的XML函数依赖的概念．它不仅能表达元素的属性和元素的值之间的函数依赖，而且也能表达元素之间的函数依赖．给出了关于XML函数依赖的一组推理规则集．     

神经网络解耦预测函数控制

结合解耦思想研究多变量系统预测函数控制。通过引入神经网络补偿环节，对多变量系统解耦，在此基础上，对解耦后各子系统进行单变量预测函数控制，以确定各个控制量。同时基于系统脉冲传递函数，得到单变量PFC控制器的显式表达式。仿真表明，该算法有较好的跟踪特性，对解决多变量系统的优化和控制具有一定的适用性。     

表达式在UGII工程图中的应用

在ＵＧＩＩ系统中建立工程图时，使用表达式常常会达到事半功倍的效果，下面就是笔者的一些心得。 一、表达式在工程图模块中变得可用 ＵＧ系统的缺省设置是在进入工程图模块后，表达式变成不可用，也就意味着，在工程图模块中不能通过更改表达式的值的方法来改变零件的模型参数。 如果需要在工程图模块中使用表达式，则只要在ＵＧ ＩＩ＿ＥＮＶ．ＤＡＴ文件中将环境变量ＵＧＩＩ－ＤＲＡＦＴ－ＥＸＰＲＥＳＳＩＯＮＳ－ＯＫ的值设置成 １。表达式对话框在制图模块中将可使用。 二、表达式用于视图比例 当有些零部件的尺寸变化较大，无法固…     

多值开关级代数在MOS电路形式验证中的应用

本文讨论了ＭＯＳ电路多值开关级代数表达式的三种标准结构，给出了将多值开关级表达式转换成布尔表达式的定理，基于这些理论，提出了ＭＯＳ电路开关级形式验证的一种方法。     

连续广义系统多点边值问题解的结构

本文在多点边值的约束条件下，讨论了连续广义控制系统解的存在唯一性及解的结构。并用Ｇｒｅｅｎ函数给出了解的表达式。     

A procedure for finding an improved upper bound on the number of optimal design points

Knowing an upper bound on the number of optimal design points greatly simplifies the search for an optimal design. Carathéodory’s Theorem is commonly used to identify an upper bound. However, the upper bound from Carathéodory’s Theorem is relatively loose when there are three or more parameters in the model. In this paper, an alternative approach of finding a sharper upper bound for classical optimality criteria is proposed. Examples are given to demonstrate how to use the new approach.     

基于Cayley图的三维六度环面网络研究

提出了一种三维六度环面Cayley图网络模型.针对该网络模型,给出了一种简单的三维节点编址方案,并利用该编址方案得到了任意两个节点间的最短距离公式;开发了一种简单的分布式最优路由算法,该算法可以运行于网络中的任意节点,可以建立任意两点之间的最短路由路径;基于陪集图(coset graph)理论,给出了一种新型的广播通信算法,并对该算法的效率进行了分析;给出了三维六度环绕网络模型直径的界限值.     

On inequalities between mutual information and variation

We continue studying the relationship between mutual information and variational distance started in Pinsker’s paper [1], where an upper bound for the mutual information via variational distance was obtained. We present a simple lower bound, which in some cases is optimal or asymptotically optimal. A uniform upper bound for the mutual information via variational distance is also derived for random variables with a finite number of values. For such random variables, the asymptotic behaviour of the maximum of mutual information is also investigated in the cases where the variational distance tends either to zero or to its maximum value.     

Analytic expressions of transfer function responses and choice ofnumerator coefficients (zeros)

General analytic expressions of transfer function responses are derived in this paper. The analytic forms include the numerator coefficients of the transfer function, a Vandermonde-like matrix, and a vector containing the transfer function eigenresponses, the latter two only depending on the eigenvalues. Several characteristics of basic transient responses are derived, e.g., their exact number of zeros. An upper bound on the number of extrema of the step response is obtained. An algorithm is suggested for the selection of the numerator coefficients, assuming fixed eigenvalues, using the derived characteristics of the basic transient responses, effectively leading to a suboptimal choice. Furthermore, the analytic formulas are used to calculate the numerator coefficients optimally, by minimizing the step transient, the ramp transient, the parabolic transient, etc. Simulations are presented indicating the properties of the basic transient responses and the transfer function response properties based on optimal and suboptimal choices of the numerator coefficients     

Online Search with Time-Varying Price Bounds

Online search is a basic online problem. The fact that its optimal deterministic/randomized solutions are given by simple formulas (however with difficult analysis) makes the problem attractive as a target to which other practical online problems can be transformed to find optimal solutions. However, since the upper/lower bounds of prices in available models are constant, natural online problems in which these bounds vary with time do not fit in the available models.We present two new models where the bounds of prices are not constant but vary with time in certain ways. The first model, where the upper and lower bounds of (logarithmic) prices have decay speed, arises from a problem in concurrent data structures, namely to maximize the (appropriately defined) freshness of data in concurrent objects. For this model we present an optimal deterministic algorithm with competitive ratio \(\sqrt{D}\), where D is the known duration of the game, and a nearly-optimal randomized algorithm with competitive ratio \(\frac{\ln D}{1+\ln2-\frac{2}{D}}\). We also prove that the lower bound of competitive ratios of randomized algorithms is asymptotically \(\frac{\ln D}{4}\).The second model is inspired by the fact that some applications do not utilize the decay speed of the lower bound of prices in the first model. In the second model, only the upper bound decreases arbitrarily with time and the lower bound is constant. Clearly, the lower bound of competitive ratios proved for the first model holds also against the stronger adversary in the second model. For the second model, we present an optimal randomized algorithm. Our numerical experiments on the freshness problem show that this new algorithm achieves much better/smaller competitive ratios than previous algorithms do, for instance 2.25 versus 3.77 for D=128.     

Optimal expansions of discrete-time Volterra models using Laguerre functions

This work is concerned with the optimization of Laguerre bases for the orthonormal series expansion of discrete-time Volterra models. The aim is to minimize the number of Laguerre functions associated with a given series truncation error, thus reducing the complexity of the resulting finite-dimensional representation. Fu and Dumont (IEEE Trans. Automatic Control 38(6) (1993) 934) indirectly approached this problem in the context of linear systems by minimizing an upper bound for the error resulting from the truncated Laguerre expansion of impulse response models, which are equivalent to first-order Volterra models. A generalization of the work mentioned above focusing on Volterra models of any order is presented in this paper. The main result is the derivation of analytic strict global solutions for the optimal expansion of the Volterra kernels either using an independent Laguerre basis for each kernel or using a common basis for all the kernels.     

Two results on tables

A.C. Yao (1981) has determined the maximal size of a finite universe U such that it is possible to store all subsets A of U with k elements in a table of k slots in such a way that membership in A can be determined in a single probe. In his model it is assumed that all elements of A are physically stored in the table. If this assumption is relaxed and arbitrary elements in U can be stored in order to encode subsets A, then Yao's upper bound is no longer valid. It fails for trivial reasons only: a single probe lookup strategy only exists when it is possible to encode arbitrary subsets of U by a bitmap.Our second result is an improvement of the optimal program size for perfect hash functions, solving an open problem from Slot and Van Emde Boas (1984): For every value u, value k ⩽ u, and every subset A of U = {0, …, u − 1} there exists a perfect hash function F which scatters A completely into a hash table of size O(k), such that the program size of F is O(k·log log k + log log u) and the evaluation time of F is O(1). These estimates are expressed in standard RAM space and instructions respectively. This improves the O(k·log k + log log u) upper bound established by Mehlhorn (1984) and Slot and Van Emde Boas (1984).     

Observer matrix gain optimization for stochastic continuous time nonlinear systems

It is shown that for a class of stationary stochastic nonlinear systems (satisfying a global Lipschitz condition) the high-gain observer with a constant gain matrix may guarantee an upper bound for the averaged quadratic error of state estimation. The nonlinearity is assumed to be a priory known. The main contribution of this paper consists in designing of a numerical procedure for the optimal gain matrix minimizing this upper bound. The convergence analysis of this procedure is presented as well as an example illustrating its finite steps workability: it is shown that within a neighborhood of the optimal matrix gain the others provide lower estimation performance.     

Guaranteed cost control for multi-inventory systems with uncertain demand

In this paper we consider the problem of controlling a multi-inventory system in the presence of uncertain demand. The demand is unknown but bounded in an assigned compact set. The control input is assumed to be also constrained in a compact set. We consider an integral cost function of the buffer levels and we face the problem of minimizing the worst-case cost. We show that the optimal cost of a suitable auxiliary problem with no uncertainties is always an upper bound for the original problem. In the special case of minimum-time control, this upper bound is tight, namely its optimal cost is equal to the worst-case cost for the original system. Furthermore, the result is constructive, since the optimal control law can be explicitly computed.     

On the design of efficient ATM routing schemes

In this paper we deal with the problem of designing virtual path layouts in ATM networks when the hop-count is given and the load has to be minimized. We first prove a lower bound for networks with arbitrary topology and arbitrary set of connection requests. This result is then applied to derive lower bounds for the following settings: (i) one-to-all (one node has to be connected to all other nodes of the network) in arbitrary networks; (ii) all-to-all (each node has to be connected to all other nodes in the network) in several classes of networks, including planar and k-separable networks and networks of bounded genus. We finally study the all-to-all setting on two-dimensional meshes and we design a virtual path layout for this problem. When the hop-count and the network degree are bounded by constants, our results show that the upper bounds proposed in this paper for the one-to-all problem in arbitrary networks and for the all-to-all problem in two-dimensional mesh networks are asymptotically optimal. Moreover, the general lower bound shows that the algorithm proposed in Gerstel (Ph.D. Thesis, Technion-Haifa, Israel, 1995) for the all-to-all problem in k-separable networks is also asymptotically optimal. The upper bound for mesh networks also shows that the lower bound presented in this paper for the all-to-all problem in planar networks is asymptotically tight.