逆

The algorithm GS to solve the problem of inverse dynamics based on the optimal theory is proposed, by using the numerical methods of Gill and shooting target, the optimal joint driven torques are obtained With the smooth joint trajectory motion, a fast and stable inverse dynamics method is proposed, it provides a new effective way to control the flexible manipulator The trajectory planning in the joint space and Cartesian coordinates is especially discussed In terms of kinematics of space flexible link manipulators, a sequential integration method for inverse dynamic analysis of flexible manipulators is developed The concrete results of simulations tested and verified the validity of proposed methods, and some valuable conclusions are achieved.

提出了求解基于最优理论的柔性臂逆动力学问题的GS法(Gill—Shooting method)，得到了柔性臂关节的最优驱动力矩；提出了基于光滑关节运动轨迹的柔性臂逆动力学的快速稳定方法，为柔性臂控制提供了一条新的途径；探讨了关节空间和直角坐标空间柔性臂的轨迹规划问题；研究并完善了结合柔性臂运动学的顺序积分的逆动力学方法。通过具体实例的仿真研究，验证了所提出的柔性臂逆动力学方法的有效性，得出了一些很有价值的结论。

A fast algorithm for calculating the inverse and Moore-Penrose inverse of the permutation factor circulant matrix is presented. Then, a fast algorithm for the product of the permutation factor circulant matrix is given. Finally, The least-square solutions of inverse problems and the optimal approximation problems for the permutation factor circulant matrix are discussed.

首先给出了一种求n阶置换因子循环矩阵的逆阵、自反g-逆、群逆、Moore-Penrose逆的快速算法，然后给出了计算两n阶置换因子循环矩阵之乘积阵的一种快速算法，最后给出了其反问题的最小二乘解的存在性定理及它的一般表示，并证明了逼近矩阵的存在唯一性且给出它的具体表达式。

The weighted Moore-Penrose inverse is a special generalized inverse which is an important basic tool in many branches of mathematics and has extensive applications in other fields such as economics, information processing, automatic control, etc. Recently, the study of generalized inverse of matrices associating with more general algebra such as ring, semiring and so on generalize the theory and methods of generalized inverse deeply and characterize the structure of algebra as well.

加权Moore-Penrose逆是一种特殊的广义逆，它不仅是许多数学分支的基本工具，而且在经济学、信息处理、自动控制等其他领域有着广泛的应用，近年来，结合环、半环等更一般的代数系统的矩阵广义逆的研究，不仅将广义逆的理论和方法作了更加深入的推广，而且也成了刻画代数结构的有力工具。

Through promoting matrix counter ,this article simply introduced the multinomial matrix ,compared with the good and bad points of the two counter algorithms in different, illustrated the utilization of counter in solving homogeneous line good equation sets, and discussed the decomposition of the Multiple polynomial matrix.

本文对逆矩阵的简单介绍后，阐述了多项式矩阵逆的定义及性质，比较了两种多项式矩阵逆的算法。讨论了在不同情况下利用逆在解线性齐次方程组的方法。最后探讨了多元多项式矩阵的分解问题。

Then, the instantaneous voltage feedback control circuit of the Z source inverter with an inner loop of the output filter inductor current is designed. The validity of the double close loop control strategy is verified by simulation and experiment results.

首先对阻抗源逆变器的逆变部分进行了建模，其次简要介绍了传统电压源型逆变器的控制策略，然后以带滤波电感电流内环的电压瞬时值反馈控制为例介绍了阻抗源逆变器的输出电压控制的实现。

The inverse polynomial and the invertible affine transformation exist by the finite field, linear algebra and matrix theory. The invertible affine transformation and the inversion in are easily realized by using lookup table. An algorithm can be used to get the inverse element of modulo .

本文运用有限域、线性代数和矩阵理论，论证了逆多项式和逆仿射的存在性，并且应用查表法简捷地实现了中元素的求逆和逆仿射变换；设计了一个易于在在计算机上实现的算法，来求形如的多项式模时的逆元，该多项式的系数在上。

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。

Secondly, the invertible assignment problem are studied. At last, we explored the conditions on the invertible completion of part matrix Mx and obtained the characterizations of the relovent operator of invertible completion.

利用构造分块初等矩阵、算子广义逆、极分解、谱分解为工具，深入地研究了算子对的逆补Mxy、算子逆配置的一系列等价刻画及一般性结论、缺项算子矩阵存在逆补Mx的等价刻画，并获得了逆补的预解集的性质刻画。

This paper studies the invariant, which is the linear preserving problem based on generalized inverse of matrices. The generalized inverse of matrices and the research status of preserving problems of generalized inverse are outlined. In the basis of deeply understanding the basic knowledge of linear maps, the definition, characteristics of generalized inverse and decomposition of matrix, the author analyzes the decomposition form of preserving idempotence and preserving tripotence in the PID, then studies on the linear maps form of preserving group inverses of symmetric matrices.

本文研究的不变量是矩阵广义逆线性算子的保持问题，概述了广义逆矩阵，广义逆保持问题的研究现状，在对线性映射的基础知识，广义逆矩阵的定义、性质和矩阵的分解深入理解的基础上，深入分析了保幂等、保立方幂等矩阵在主理想整环上的分解形式，继而研究了保对称矩阵群逆的线性算子形式。

Study on west Namco thrust Three ductile shear zones were discovered in Gayalong, Elongnubu and Shenjue-Gechangchayu, and geological features, deformation, motion direction and structural pattern are studied in detail for major thrust faults, ductile shear zones and folds in west bank of Namco Lake, leading to identification of west Namco thrust . And west Namco thrust and ophiolite mélanges outcropped from west Namco Lake to Yongzhuzangbu coexist together, indicating another tectonic suture in the Tibetan Plateau termed as the Namco-Yongzhu suture or NYS with its east extension to Jiali fault.

纳木错逆冲推覆构造研究：发现纳木错西岸嘎龙垭韧性变形带、饿弄怒布舍糜棱岩带和生觉—各昌茶玉韧性剪切带，详细观测典型逆冲断层的地质特征、变形特点、运动方向和序次关系，分析逆冲断层、褶皱构造、韧性剪切带的几何配置关系和动力学成因联系；分析纳木错逆冲推覆构造的空间影响范围，向东延伸与嘉黎逆冲断裂相连接，向西延伸与果忙错—永珠藏布构造带相归并，与纳木错西岸蛇绿岩、永珠藏布—果忙错蛇绿岩共同组成拉萨地块中部最重要的区域构造，命名为纳木错—永珠缝合带。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。