随机函数

The property of continuous function and the formula of probability addition to the convergence in probability of continuous function sequence of random vector is used.

摘要将依概率收敛的一维随机变量序列的连续函数仍依概率收敛的结论推广到随机向量序列的情形。

Via the stochastic averaging method, the four-dimensional system is reduced to a two-dimensional one. Through the logarithmic polar transformation , and then Girsanov theorem and Feynmann-Kac formula, the backword differential operator is then obtained. By expanding the eigenfunctions as a Fourier cosine series, the approximate analytic expansion of the moment Lyapunov exponent is then obtained.

首先在经典二元机翼颤振方程加入随机激励，通过随机平均法，Girsanov定理和Feynmann-Kac公式得到关于矩Lyapunov指数的特征值问题，其次采用Fourier余弦级数对特征函数进行正交展开得到系统矩Lyapunov指数的近似解析式。

Based on product moment of normal random variable cariable calculating covariance function of square of normal stochastic process has been given.

在正态随机变量乘积矩基础上，给出了正态随机过程平方后的协方差函数的计算。

This term studies mainly the applications of Theory of covering surface in differential equations, potential theory, complex dynamics and several complex variables, and researches the analysis and geometry properties of random Taylor series and random Dirichlet series.

本项目主要研究覆盖曲面理论及其在微分方程、位势理论、复解析动力系统以及多复变函数中的应用；研究随机泰勒级数、随机狄里克莱级数的分析性质和几何性质。

Basic concepts of stochastic processes: family of finite dimensional distribution functions, numerical characteristics of stochastic processes.

随机过程的基本概念：有限维分布函数族，随机过程的数字特征。

A convergence of the section sum in stochastic sequence under finite state is produced with the help of same distribute and comparative function of stochastic sequenct.

利用随机序列的同分布性及比较函数，导出了有限状态随机序列部分和的一个收敛性质。

A function of a random variable is itself random in general.

一个随机游走的函数其本身也是随机的。

This paper presents the mechanism of erosion scour around groynes of levee projects and a probability method of the reliability analysis for groyne erosion under random factors.

分析了防护丁坝冲刷的机理，用概率分析方法研究了在随机因素影响下防护丁坝抗冲刷的可靠性问题。应用Rosen-blatt变换确定防护丁坝抗冲刷破坏的功能函数在随机因素影响下的可靠性指标。

Relying on the mass function, the relations are studied between belief measure and plausibility measure of incoordinate objective random information systems and positive domain reduction and distribute reduction of incoordinate objective information systems.

借助mass函数，研究了不协调的目标随机信息系统中信任测度和似然测度分别与不协调的目标信息系统的正域约简和分配约简的关系，得到了不协调的目标随机信息系统基于证据理论的正域约简和分配约简的方法。

In our thesis, contents are organized as following In Chapter 1 we present our topic's internal and overseas research situations, theoretical and practical significance, and introduce the research object and contents, and the main contributions of this dissertation. Chapter 2 reviews the development of the stability results for nonlinear systems and some relevant recent results, which include Lyapunov and LaSalle-Yoshizawa theorems for nonlinear systems, and stochastic edition for stochastic nonlinear systems. Sontag's formula for systems affine in control is presented in the frame of CLF. The concepts of disturbance attenuation and the inverse optimality are also explained in this Chapter. In chapter 3 we present the solvable theorem of inverse optimal gain assignment problem, design the inverse optimal controller and the inverse optimal tracking controller for strict-feedback nonlinear continuous systems with unknown time-varing bounded disturbances and constant unknown parameters using an adaptive backstepping algorithm, which are nonlinear, continuous and are easier to realize. These designs are fully systematic and the algorithm can be directly coded in symbolic software. The results of simulation show the effectiveness of the control algorithms.

论文的结构如下：在第1章中，给出了本文研究课题的研究现状、理论意义和实际应用，并介绍了本文的研究对象、研究内容以及主要贡献；在第2章中，针对确定性非线性系统和随机非线性系统，分别介绍了Lyapunov定理、LaSalle-Yoshizawa定理及其随机版本；对仿射系统，在控制Lyapunov函数框架下，给出了Sontag公式；同时给出了非线性系统扰动抑制和逆最优控制问题的基本概念；在第3章中，针对具有未知时变有界扰动和未知定常参数的一类不确定非线性系统，给出并证明了逆最优增益配置可解定理，使用自适应Backstepping算法和均值定理，系统地设计了自适应逆最优控制器和逆最优跟踪器，这种设计方法可同时获得逆最优控制策略和自适应律，简单明了，仿真结果表明该控制算法的有效性，并给出了性能估计。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。