仿射函数

With the example of the chaos game, a parallel algorithm is designed for this kind of recurrence question by bisection method.

通过对含有概率的迭代函数系统的仿射变换系数进行改造，将IFS的动态迭代问题静态化，使之成为典型一阶线性递推问题。

Under some assumption conditions, we also developed trust region and affine scaling algorithm and potential reduction algorithm for convex programming problem with linear constraints.

然后在一定的假设条件下，对线性约束下的凸规划问题我们给出了相应的信赖域仿射尺度算法和势函数下降算法。

Due to the non-affine form of the control inputs, feedback linearization method can not be used to design control system. Therefore, implicit function theorem is firstly exploited to assert the existence of the ideal control inputs, which can compel the system outputs to track their desired trajectories, and then ideal control inputs are constructed.

由于该系统的控制输入为非仿射形式，不能采用反馈线性化的方法设计控制系统；因此，首先采用隐函数定理证实了能够使系统输出跟踪期望轨迹的理想控制输入的存在性，并构造了理想的控制输入。

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。

Corresponding mathematics model was developed, hole-edge stress analysis on composite material plate with multiform holes was carried out, accurate boundary conditions was founded by conformal mapping method, boundary problems of the two stress functions could be treated by affine transformation in the same way synchronously.

建立了相应的数学模型，对含不同孔型复合材料板进行了孔边应力分析，通过保角映射方法建立精确的边界条件，解决了复杂孔型的边界条件问题，借助仿射变换能同时并且同方法的处理这两个应力函数在边界上的问题。

Firstly, a class of affine nonlinear systems are considered. The single-layered neural networks are used to approximate the nonlinear functions of the systems. Stable adaptive control algorithms are presented based on system states feedback and system output feedback respectively. The boundary of the tracking error is guaranteed. Then, by using the technique of input-output linearization, the stable adaptive control method for general nonlinear systems is proposed. Finally, the effectiveness of the proposed adaptive control algorithms are verified through the simulation researches for the control of robot manipulator.

首先考虑一类仿射非线性系统，利用单层神经网络去逼近系统的非线性函数，分别给出了基于系统状态反馈和输出反馈的稳定自适应控制算法，确保系统的跟踪误差有界；然后利用输入输出线性化方法，给出广义非线性系统的自适应控制方法；最后通过在机械手位置跟踪控制中的仿真研究，验证了所提方法的有效性。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失