静止无功发生器的微分几何变结构控制方法

根据静止无功发生器(SVG)数学模型的非线性特性,提出了微分几何变结构控制方法,运用微分几何精确线性化理论,把非线性系统转化成了一个线性系统,在此基础上应用非线性变结构控制理论进行设计控制器。结果表明,微分几何变结构控制方法对补偿SVG的无功电流具有有效性和可行性。     

非线性系统的几何方法（下） 目前动态与展望

本文的第一部分介绍了几何方法的背景。这一部分介绍目前的进展情况及今后的发展趋势。 四、目前研究的几类课题 本节介绍非线性系统几何方法研究的几类课题,包括主要结果,进展情况和存在的问题。     

微分几何方法与非线性控制系统（4）

7 非线性控制系统的几何理论 7.1 非线性控制系统的几何描述 定义在R~n上的一般非线性系统可以用微分方程描述如下: x=f(x,4) (7.1a) y=h(x) (7.1b)这里,状态x∈R~n;控制u∈R~m;输出y∈R~r,等式(7.1a)称为状态方程,(7.1b)称为输出方程。为了便于使用微分几何的工具,假设f对x和u都是光滑或解析函数,同样,h(x)也是C~∞     

动态逆方法和微分几何反馈线性化方法的对比

简述了非线性反馈线性化的微分几何方法和动态逆方法的基本原理,然后分析了这两种方法的理论联系,说明对仿射非线性系统,这两种方法在本质上是一致的.最后对这两种方法进行了有益的比较,并阐明了二者的联系和区别.     

微分几何理论在非线性解耦和线性化中的应用

非线性系统的微分几保控制理论的形成和发展给非线性控制的研究带来了一系列理论上的突破和成果，本文综了近年来微分几何理论在非线性系统解耦控制和线性化方面的应用状况。     

动态逆方法和微分几何反馈线性方法的对比

简述了非线性反馈线性化的微分几何方法和动态逆方法的基本原理，然后分析了这两种方法的理论联系，说明对仿射非线性系统。这两种方法在本质上是一致的。最后对这两种方法进行了有益的比较，并阐明了二者的联系和区别。     

微分几何方法与非线性控制系统（1）

近年来,微分几何方法作为一种新的工具,被引入控制系统特别是非线性控制系统的研究中,并得到很大发展,正如Isidori在中所说:“近10年来,微分几何方法对于非线性系统的研究证明是成功的,这就象50年代研究单输入单输出线性系统所用的拉氏变换及复变函数,60年代研究多变量线性系统用线性代数那样”。 因此,从某种意义上说,微分几何方法的引入,标志着控制理论发展的一个新阶段。     

基于LabVIEW数控机床几何误差补偿的研究方法

介绍一种由软件、硬件控制的数控机床几何误差补偿。误差补偿的原理主要是运用多体系统运动学理论建立机床几何误差模型,用硬件控制固化在程序存储器内的误差补偿程序完成补偿任务,并通过RS-232C实现数控机床与Windows平台通信与数据交换。     

共形几何代数--几何代数的新理论和计算框架

共形几何代数是一个新的几何表示和计算工具.作为几何的高级不变量和协变量系统的结合,它为经典几何提供了统一和简洁的齐性代数框架,以及高效的展开、消元和化简算法,从而可以进行极其复杂的符号几何计算,在几何建模与计算方面表现出很大的优势.主要讲述共形几何代数的产生背景和意义,共形几何代数的数学理论和它最有特色的几个部分,包括Grassmann结构、统一几何表示和旋量作用、基本不变量系统和高级不变量系统、新的计算思想、展开和化简技术等.     

微分几何方法与非线性控制系统（2）

4 向量场与动态系统 众所周知,现代控制理论的研究是在状态空间上,使用状态方程,但有些动态系统,特别是非线性系统,其动态演变是在微分流形上进行的,演化结果是流形上的一条曲线,描述无穷小演化的微分方程是定义在流形上的向量场,因此,研究流形上的动态系统,就要分析流形上的向量场。流形上向量场的局部坐标表示是R~n中的微分方程组。在状态空间中,向量场就是状态方程的几何解释。应用向量场来研究动态系统的方法,就是几何方法。     

Geometric constraint solving with conics and linkages

Most geometric construction methods of geometric constraint solving systems use line and circle (rule and compass) as basic drawing tools. In this paper, by introducing conics and linkages, we provide a set of complete drawing tools for the construction approach of geometric constraint solving. Using these tools, we may enlarge the drawing scope of the construction approach and still keep the elegant style of geometric solutions to geometric constraint solving. As applications, we obtain pure geometric solutions to three sets of well-known constraint problems: the 10 Apollonian drawing problems, the 13 cases of a smallest tri-connected constraint graph, and constraint problems with distance constraints only.     

非线性系统研究动态与展望

本文对近几年非线性控制系统的进展情况作了综合报导。文章共分三个部分:第一部分强调:什么是反馈意义下的非线性系统;第二部分介绍了近几年非线性控制系统研究中较集中的八个方面的问题;第三部对非线性控制理论今后主要研究动向作了预测。     

Geometric approach to non-linear optimal control problems

Minimum energy control problems are investigated for affine non-linear systems evolving on manifolds, in the framework of the geometric theory of hamiltonian systems. Some insights into the problems are gained via this machinery.     

Modeling multibody systems with uncertainties. Part II: Numerical applications

This study applies generalized polynomial chaos theory to model complex nonlinear multibody dynamic systems operating in the presence of parametric and external uncertainty. Theoretical and computational aspects of this methodology are discussed in the companion paper “Modeling Multibody Dynamic Systems With Uncertainties. Part I: Theoretical and Computational Aspects”.In this paper we illustrate the methodology on selected test cases. The combined effects of parametric and forcing uncertainties are studied for a quarter car model. The uncertainty distributions in the system response in both time and frequency domains are validated against Monte-Carlo simulations. Results indicate that polynomial chaos is more efficient than Monte Carlo and more accurate than statistical linearization. The results of the direct collocation approach are similar to the ones obtained with the Galerkin approach. A stochastic terrain model is constructed using a truncated Karhunen-Loeve expansion. The application of polynomial chaos to differential-algebraic systems is illustrated using the constrained pendulum problem. Limitations of the polynomial chaos approach are studied on two different test problems, one with multiple attractor points, and the second with a chaotic evolution and a nonlinear attractor set.The overall conclusion is that, despite its limitations, generalized polynomial chaos is a powerful approach for the simulation of multibody dynamic systems with uncertainties.     

Geometric state-space theory in linear multivariable control: A status report

With the renewed emphasis in control theory on qualitative structural issues, as distinct from techniques of optimization, the last decade has brought significant growth in the application of geometric ideas to the formulation and solution of problems of controller synthesis. In this article we review the status of geometric state space theory as developed for application to systems that are linear, multivariable and time-invariant. After a brief summary of the underlying geometric concepts ((A, B)-invariant subspaces and (A, B)-controllability subspaces) we outline two standard problems of feedback control that have been successfully attacked from this point of view, and briefly survey recent results in a range of other topic areas. Then we discuss certain issues of methodology, and conclude with some remarks on computational procedures.     

Geometric neural computing

This paper shows the analysis and design of feedforward neural networks using the coordinate-free system of Clifford or geometric algebra. It is shown that real-, complex-, and quaternion-valued neural networks are simply particular cases of the geometric algebra multidimensional neural networks and that some of them can also be generated using support multivector machines (SMVMs). Particularly, the generation of radial basis function for neurocomputing in geometric algebra is easier using the SMVM, which allows one to find automatically the optimal parameters. The use of support vector machines in the geometric algebra framework expands its sphere of applicability for multidimensional learning. Interesting examples of nonlinear problems show the effect of the use of an adequate Clifford geometric algebra which alleviate the training of neural networks and that of SMVMs.     

Decomposition Plans for Geometric Constraint Systems,Part I: Performance Measures for CAD

A central issue in dealing with geometric constraint systems for CAD/CAM/CAE is the generation of an optimal decomposition plan that not only aids efficient solution, but also captures design intent and supports conceptual design. Though complex, this issue has evolved and crystallized over the past few years, permitting us to take the next important step: in this paper, we formalize, motivate and explain the decomposition–recombination (DR)-planning problem as well as several performance measures by which DR-planning algorithms can be analyzed and compared. These measures include: generality, validity, completeness, Church–Rosser property, complexity, best- and worst-choice approximation factors, (strict) solvability preservation, ability to deal with underconstrained systems, and ability to incorporate conceptual design decompositions specified by the designer. The problem and several of the performance measures are formally defined here for the first time—they closely reflect specific requirements of CAD/CAM applications. The clear formulation of the problem and performance measures allow us to precisely analyze and compare existing DR-planners that use two well-known types of decomposition methods: SR (constraint shape recognition) and MM (generalized maximum matching) on constraint graphs. This analysis additionally serves to illustrate and provide intuitive substance to the newly formalized measures. In Part II of this article, we use the new performance measures to guide the development of a new DR-planning algorithm which excels with respect to these performance measures.     

Geometric Information Criterion for Model Selection

In building a 3-D model of the environment from image and sensor data, one must fit to the data an appropriate class of models, which can be regarded as a parametrized manifold, or geometric model, defined in the data space. In this paper, we present a statistical framework for detecting degeneracies of a geometric model by evaluating its predictive capability in terms of the expected residual and derive the geometric AIC. We show that it allows us to detect singularities in a structure-from-motion analysis without introducing any empirically adjustable thresholds. We illustrate our approach by simulation examples. We also discuss the application potential of this theory for a wide range of computer vision and robotics problems.     

Geometric nonlinear analysis of flexible spatial beam structures

An updated Lagrangian formulation of the spatial beam element is presented for a purely geometric nonlinear analysis in which the geometric stiffness matrix is expressed either by a one-dimensional integration of the stress resultants or by a closed form of element-end forces. A computer code, NACS, is developed based on this formulation which has a number of facilities to meet the special requirements for the analysis of suspension and cable-stayed bridges. Several example problems are reported.     

Passivity,Feedback Equivalence and Global Stabilization of Nonlinear Markovian Jump Systems

This paper combines the passivity theory with geometric control theory for nonlinear Markovian jump systems. The key point concentrates on taking the appropriate coordinate changes following with the Markovian switchings. Based on this concept, we investigate the passivity, feedback equivalence and global stabilization problems, which implies that under a proposed strongly minimum‐phase condition, the nonlinear Markovian jump system is feedback equivalent to a passive system. A numerical example is presented to illustrate the effectiveness of our results.