ON UNILATERALLY CONSTRAINED MOTIONS OF RIGID BODIES SYSTEMS

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Residue integrals and Waring’s formulas for algebraic or even transcendental systems

The present article is focused on the study of a special class of systems of non-linear transcendental equations for which classical algebraic and symbolic methods are inapplicable. For the purpose of study of such systems we develop a method for computing residue integrals with integration over certain cycles. We describe conditions under which the mentioned residue integrals coincide with power sums of the inverses to the roots of a system of equations (i.e. multidimensional Waring’s formulas). Based on this, we develop an algorithm that computes such power sums without computing the roots. As an application of the suggested method, we consider a problem of finding sums of multi-variable number series.     

模糊推理的变权综合算法及其构造的模糊系统响应能力分析

将变权综合原理应用于模糊推理,提出一种新的模糊推理算法-变权综合推理算法,并给出利用模糊蕴涵算子确定规则变权的方法。证明了由一些正常蕴涵算子如Lukasiewicz蕴涵、Goguen蕴涵、Godel蕴涵、Dubois-Prade蕴涵等确定的变权综合算法是相容的。进一步分析了该变权综合算法构造的模糊系统的响应能力,结果表明:基于这些正常蕴涵算子的变权综合算法构造的模糊系统具有泛逼近性。     

两类模糊系统作为通用逼近器的充分条件的比较与分析

对现有的Mamdani模糊系统和T-S模糊系统作为通用逼近器的充分条件作比较分析,提出了通过三种不同算法获得的单输入单输出Mamdani模糊系统作为通用逼近器的充分条件的保守性比较定理。     

具有数据丢失的网络化控制系统的基于观测器的镇定

研究具有数据丢失的网络化控制系统的基于观测器的镇定问题。受控对象是由T-S模糊模型描述的非线性时滞系统。把数据丢失过程建模成独立同分布过程。利用模糊Lyapunov函数方法得到了闭环系统随机稳定的充分条件,其基于观测器的反馈控制器可通过求解一组线性矩阵不等式来设计。一个仿真例子说明方法的有效性。     

一般非线性控制系统的最小Hamiltonian实现问题研究

本文给出了一般非线性控制系统的最小Ｈａｍｉｌｔｏｎｉａｎ实现的存在性条件和唯一性结果。     

State space calculations for discrete probability densities

State space methods have proved to be powerful theoretical and computational tools in a number of areas of applications, in particular filtering and control theory. In this paper we advocate the use of state space methods for the study of discrete probability densities on the set {0,1,2,…}. The fundamental approach is to consider the class of all discrete probability densities that can be represented as the impulse response/convolution kernel of a finite dimensional discrete time state space system. We show that all standard operations such as the calculation of moments, convolution, scaling, translation, product, etc. can be carried out using system representations.     

不确定离散时滞模糊系统的保性能控制

针对一类模糊模型表示的，具有范数有界时变参数不确定性离散时滞系统，研究了保性能控制器设计问题。首先推导了保性能控制器存在的充分条件，在此基础上通过求解等价的线性矩阵不等式给出了控制器的设计方法和参数表示。     

Kinetic Limit for a System of Coagulating Planar Brownian Particles

We study a model of mass-bearing coagulating planar Brownian particles. The coagulation occurs when two particles are within a distance of order ε. We assume that the initial number of particles N is of order |logε|. Under suitable assumptions of the initial distribution of particles and the microscopic coagulation propensities, we show that the macroscopic particle densities satisfy a Smoluchowski-type equation.