系统函数

In this paper, by using the method of expanding the hard-edge aperture function into a finite sum of complex Gaussian functions, the recurrence propagation expression for the propagation of partially coherent beams through a multiple apertured ABCD optical system is derived, which provides a fast algorithm for simulating the propagation of partially coherent beams through hard-aperture optics.

用有限个复高斯函数之和来逼近硬边光阑窗函数的方法，推导出了部分相干光通过多个硬边光阑ABCD光学系统传输的递推公式，提供了一种模拟部分相干光通过硬边光学系统传输的快速算法。

First low order approximation of generating function and approximate optimal trajectory were obtained. Then using low order approximation of generating function of Hamilton "relative motion" to the approximate optimal trajectory, improvement of the approximate optimal trajectory was iteratively made. In this way, high order approximation accuracy can be obtained by only using low order approximation, which is much cost effective in computing.

首先以较低的计算代价，获得最优控制Hamilton系统生成函数的低阶近似，得到一条近似的最优轨线，然后将最优控制Hamilton系统相对于近似最优轨线求"相对运动"，该"相对运动"仍具有Hamilton性质，利用这一"相对运动"的生成函数低阶近似，可以对近似最优轨线进行迭代修正，从而以计算代价较小的低阶近似逼近计算代价高得多的高阶近似的精度。

These models include logarithmic function, exponential function, hyperbolic function and system scientific models such as grey model, BP neural network, time series, kalman filter and so on. And ground settlement due to two box culvert pushing is simulated by Peck experiential formula.

3介绍了地下工程中常用的数据分析建模方法并给出应用实例，包括概率统计模型中的对数函数、指数函数、双曲函数，系统科学中的灰色系统、BP神经网络、时间序列、Kalman滤波等，利用Peck公式对双孔箱涵错距顶进引起的地表沉降进行了模拟。

For delay discrete-time linear system, saturant function is introduced. Thesufficient condition of GAS and RAS is presented by saturant function infimum.

针对时滞离散线性系统，引入饱和函数，利用饱和函数的下确界，建立了系统全局渐近稳定和局部渐近稳定的充分条件。

Sensitivity function and control sensitivity function are obtained by Youla parameterization of controller,which is used to describe an integral square performance criterion containing tracking error and control energy.

由控制器Youla参数化得到控制系统的敏感度函数和控制敏感度函数用来表示一个包含跟踪误差和控制能量在内的积分平方性能指标，针对不同类型的时滞过程运用谱分解的方法最小化该性能指标，从而导出相应控制器的设计方法，可使系统在控制能量约束条件下具有最优的控制性能。

Based on this notion and the invariance principle, a condition is proposed and proved, under which an invariant set of states of a switched system with Lyapunov stable subsystems can be stabilized by state feedback.

基于这个不变性原理以及输入对系统能量函数稳定的概念，利用多Lyapunov函数方法提出并证明了一类具有Lyapunov稳定子系统的切换系统的不变集可状态反馈镇定的条件。

In Chapter 4 we discuss the solvable theorem of adaptive inverse optimal control problems, and proceed with controller designs of global asymptotic stability in probability, adaptive inverse optimal stabilization in probability and output-feedback adaptive inverse optimal stabilization in probability for strict-feedback stochastic nonlinear continuous systems with additive standard Wiener noises and constant unknown parameters using It〓's differentiation rule and an adaptive backstepping algorithm. Control laws and adaptive laws can be obtained at one time by this design scheme. Many simulations have been performed to validate the properties of the proposed adaptive control scheme.

在第4章中，针对具有标准Wiener噪声扰动和未知定常参数的不确定随机非线性系统，提出并证明了自适应逆最优控制问题可解定理，构造了适当形式的四次型随机控制Lvapunov函数，基于It〓微分规则和自适应Backstepping算法，系统地设计了全局依概率渐近稳定控制器、自适应逆最优控制器、输出反馈逆最优控制器以及在设计中如何处理二阶Hessian矩阵函数的方法，这种方法可同时获得控制律和自适应律，通过实例仿真，表明该控制算法是有效性的。

We also present iterated function systems 、local iterated function systems、Barnsley's collage theorem and Markov's theorem.

我们也介绍了迭代函数系统、局部迭代函数系统、Barnsley的拼贴定理和Markov定理。

The basic principle and the action of accompanied probability in iteration function system are introduced.

介绍了迭代函数系统的基本理论以及伴随概率在迭代函数系统中的作用。

First,this problem is converted into the problem of H_2 opmization constrainedby H_∞performance and pole location,then an auxiliary perfomance function is introduced,andthe former problem can be converted into the optimal problem of minimization of the auxiliaryperformance function with constraints described by a matrix equation,at Jast this problem issolved by lagrange multipliers,and the static output feedback controllers are designed.

首先将文题转化为一个具有H＿∞性能和系统闭环极点位置约束的系统H＿2性能优化问题。进而通过引入一个辅助性能函数，将其转化成有一个矩阵方程约束的辅助性能函数的最小化优化问题，并给出这个问题静态输出反馈控制器的解。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷