仿射参数

New techniques that utilize a Lyapunov function with affine dependence on the uncertain parameters to replace the fixed Lyapunov function are developed to make the criteria less conservative. It extends the approach of robust H(subscript ∞) performance of time-invariant descriptor systems.

该方法利用依赖于仿射的带有不确定参数的Lyapunov函数代替固定Lyapunov函数，来降低设计的保守性，是研究时不变广义系统的鲁棒H性能方法的推广。

New techniques that utilize a Lyapunov function with affine dependence on the uncertain parameters to replace the fixed Lyapunov function are developed to make the criteria less onservative.

该方法利用依赖于仿射的带有不确定参数的Lyapunov 函数代替固定Lyapunov 函数，来降低设计的保守性，是研究时不变广义系统的鲁棒H∞性能方法的推广。

Non linear ; fractal ; self affine ; target recognition ; parameter extraction

非线性；分形；自仿射；目标识别；参数提取

The new algorithm is based on nonlinear dense estimation and applies the affine model.

新算法是基于非线性密度进行估计的，采用了六参数的仿射模型。

It has been widely used in recent years, for it not only preserves several advantages of B-spline surface, especially the affine- invariance, but also has some special advantages such as adaptability to arbitrary topology which parameter surface doesn't have.

它不仅具备B样条曲面仿射不变性等良好性质，还具有参数曲面所没有的任意拓扑适应性等特点，因而近年来得到了广泛的应用。

This technology not only preserves the properties of localness and affine-invariance of B-spline surface, but also has some special advantages such as adaptability to arbitrary topology which parameter surfaces dont have. These good qualities makes subdivision surface used widely in recent years.

它不仅具备B样条曲面的局部支承性、仿射不变性等良好性质，而且具有参数曲面所没有的任意拓扑适应性等特点，因而近年来得到广泛的应用。

Furthermore,some circular arc spline curves which have C~0 or GC~1 continuity are constructed.

该表示形式中没有权因子和额外的控制参数，而且具有几何不变性、仿射不变性等良好性质。

Then, the minutiae sets are aligned globally through coordinate transform, and the alignment parameters are optimized by using affine transform and least square method. Finally, minutiae matching and directional field matching are respectively achieved based on the minutiae alignment, and the two matching scores are fused into a single to obtain a more reasonable result. Experimental results show that this method contributes to ensure the accuracy of fingerprint identification as well as possesses the real-time performance.

该算法首先利用脊线信息快速确定满足局部匹配要求的细节点对，在此基础上进一步通过全局坐标变换完成细节点的全局配准，并采用仿射变换模型通过最小二乘估计对配准参数进行优化，然后在配准的基础上分别进行细节点匹配和方向场匹配，最后对两种匹配分值进行融合，以取得较合理的匹配结果。

The fundamental compute region B is determined and self-similarly mapped into the upper half plane by using the homeomorphic affine transformationθ, so the fractal images of the upper half plane, square limit, and circle limit can be constructed.

周期化动力平面或参数平面，确定基本计算区域，应用同胚仿射变换将基本计算区域自相似地映射到上半平面，进而构造方极限和圆极限分形图。

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。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。