考虑免疫反应损害的细胞-细胞病毒动力学模型的确定和随机稳定性分析

利用Lyapunov函数方法研究了在免疫反应损害情况下的细胞细胞病毒动力学模型的确定稳定性和随机稳定性.当基本再生数R0≤1,病毒在体内清除;而R0>1时,病毒在体内持续生存.并且模型的正平衡点在随机扰动下也是稳定的.     

ADAPTIVE SYSTEMS THEORY： SOME BASIC CONCEPTS, METHODS AND RESULTS

The adaptive systems theory to be presented in this paper consists of two closely related parts: adaptive estimation (or filtering, prediction) and adaptive control of dynamical systems. Both adaptive estimation and control are nonlinear mappings of the on-line observed signals of dynamical systems, where the main features are the uncertain-ties in both the system‘s structure and external disturbances, and the non-stationarity and dependency of the system signals. Thus, a key difficulty in establishing a mathematical theory of adaptive systems lies in how to deal with complicated nonlinear stochastic dynamical systems which describe the adaptation processes. In this paper, we will illustrate some of the basic concepts, methods and results through some simple examples. The following fundamental questions will be discussed: How much information is needed for estimation? How to deal with uncertainty by adaptation? How to analyze an adaptive system? What are the convergence or tracking performances of adaptation? How to find the proper rate of adaptation in some sense? We will also explore the following more fundamental questions: How much uncertainty can be dealt with by adaptation ? What are the limitations of adaptation ? How does the performance of adaptation depend on the prior information ? We will partially answer these questions by finding some “critical values“ and establishing some “Impossibility Theorems“ for the capability of adaptation, for several basic classes of nonlinear dynamical control systems with either parametric or nonparametric uncertainties.     

发展中国家电力市场的定价之二——随机型当量电价的次日上网定价和运作

本文指出在次日上网电价预测中有必要引入随机生产模拟技术和可靠性指标控制,特别是对电力短缺的电力市场和担当峰负荷发电厂商的上网定价更有必要．本文将“确定型当量电价的次日上网定价和运作”发展为随机型,其中最主要贡献是：（１）推荐采用累积量法的随机生产模拟方法,以适应多变的电力市场;（２）将随机生产模拟与一维搜索寻优交替进行,从而发展了一个适用于次日上网定价的随机型优化模型ＶＡＧＳ－４,并引入了可靠性水平控制;（３）导出了随机情况下边际容量成本的解析表达式,这就构成了一个完整的、更精致的随机型当量电价的次日上网定价方法．最后给出了数字算例,并与确定型方法的算例作了比较     

基于泊松过程的 ATM 网 VBR 视频业务新模型

提出了一种新的ＶＢＲ视频业务模型：Ｇａｍｍａ到达的双泊松随机过程．该模型的分形维数小于１,具有长时相关性,能较好地描述具有突发性的实际数据业务,而且具有参数少、形式简单、便于分析等特点．由于其建立在传统的泊松过程上,给进一步对该模型进行排队分析带来了极大的方便．较详细地分析了这一新模型及其参数,得出了一些重要结论．     

Stability Robustness Bounds of Stochastic Linear Systems with Delayed Perturbations

This note considers stability robustness bounds on a classof stochastic linear systems with delayed perturbations.Using the stochastic Lyapunov stability theory,severalsufficient conditions for delay-independent stochasticasymptotic stability are obtained.It is shown that if theperturbation terms satisfy some conditions,then the sto-chastic systems have the robustness.     

证券投资中的模糊决策

根据多种证券收益率的统计数字,利用模糊多目标规划技术,给出一个新的证券投资决策模型。该模型的目标函数及其约束函数均为模糊数,它克服了文献［１～５］中模型系数为常量的缺陷,使其符合于预期收益率和投资风险的非稳定性     

Rattling系统的一种随机模型

研究了一个叠加噪声的Rattling系统.代替常用的数值分析方法,采用非高斯截断技术导出一个由平均映射描述的离散随机模型．实例指出该模型能揭示浑沌随机性质,可用于模拟齿轮箱噪声源     

基于随机Petri网可修控制系统的可用度计算

提出了一种基于随机Ｐｅｔｒｉ网的可修控制系统的稳态可用度的计算方法。该方法利用随机Ｐｅｔｒｉ网作工具来分析系统的状态变化关系，从而得出相应的Ｍａｒｋｏｖ链状态转移图，再利用由此得来的状态概率矩阵方程求解，计算较为简单。     

连续随机系统的变结构控制

研究一般连续型Ｉｔｏ随机系统的变结构控制，构造了滑动流形，给出了变结构控制律，文末的算例示范了本文结果的应用方法     

返滴定法测鞣液中的三价铬

本法是用EDTA络合返滴定直接测量皮革鞣液中的三价铬,与仪器分析法和传统的碘量法比较,有经济、省时、易掌握、准确度较高的优点,特别是在测量过程中不需将三价铬氧化为毒性较大的六价铬,从而一定量地避免了环境污染。