边值系统的能控性与能观测性问题

把抽象系统的能控性和能观测性推广到由强连续双半群描述的抽象边值系统,给出了相应的边值系统能控性的充要条件,并研究了能观测性与能控性之间的对偶关系.最后作为例子,研究了双曲系统能控性.文中所得的结果可用于讨论现代物理系统中出现一类边值系统的能控性与能观测性问题.     

弹性振动的闭环系统

细长体的飞行器在飞行中考虑了既有刚性运动又有弹性振动的运动,由于刚性运动对弹性振动的影响,通过安装在飞行器上面的仪表所测得的角速度作为反馈信号输入到控制器,由控制器输出端输出信号到执行机构来实现反馈控制,把刚性运动飞行器、弹性振动飞行器同时考虑作受控对象,这里我们研究了由刚性飞行器、弹性飞行器和控制器三者形成的闭环系统的弹性振动问题,得到了求闭环系统的频率和振型的公式,设计控制器使得闭环系统渐近稳定的条件和能控性、能观测性的条件。     

关于随机能控性

在确定性控制系统中,完全能控性是讨论把任意的初始状态控制到零的问题。在随机控制系统中,相应的概念应该是什么?在[2、3]中,引进了随机能控性的概念,但是当随机控制系统退化为确定性控制系统时,在[2、3]中所讨论的随机能控性,并不就是相应的     

非线性开关控制系统的能控性

本文研究了一类具有不同控制器的非线性开关控制系统的能控性问题.利用了几何控制的方法和Kalman秩条件,获得了这类控制系统的能控性结果,推广了E.Zuazua在参考文献[7]中的结论.     

椭圆-抛物系统的近似能控性

设计了两类控制器同时作用于椭圆-抛物系统:一类是传统的内部控制(分布控制器);另一类是以一个时变系数形式描述的内部控制(块控制器,κ(t)只是和时间有关,而与空间位置x没有关系,所以称块控制器,是相对于分布控制而言的).由于这里讨论的系统是非线性的,也只能得到全局近似能控性,不能得到精确零能控性.设计这样的控制器的目的...     

一类无穷维线性控制系统的能控性

§1.引言分布参数系统的能控性与能观测性吸引了许多作者的注意(例如见[1,2]),与有穷维情形相仿,形如(1)的无穷维线性控制系统的能控性和能观测性讨论得最多也最充分。     

分布参数控制系统的能控性、能观测性

自五十年代末期在空间技术发展的基础上,自动调节原理发展成现代控制理论。在六十年代初现代控制理论形成初期出现了能控性、能观测性两个基本概念。对工程系统的哪些特征量进行量测,就足以确定系统的金部状态?这就是能观测性问题,对工程系统的哪些状态加以控制,就足以把系统引向     

随机能观测性的等价条件

<正> 在文献[1]中给出了连续时间线性随机系统的随机能观测和随机能检测的定义,给出了判别随机能观测的充分必要条件,但对随机能检测性只给出了判别它的充分条件,并没有给出充分必要条件.同时判别随机能观测性的条件也比较不好验证.本文将证明系统随机能检测等价于随机能观测,并将列出几个等价的判别准则.     

一般型数字最优预见伺服系统的设计

在最优预见伺服系统设计中通常只考虑阶跃型目标值函数．本文研究当自标值信号及干扰信号为多项式或为线性齐次系统的输出时最优预见伺服系统的设计问题，得到了如下三方面的结果：（一）扩大系统的能控性及能观测性条件；（二）最优预见控制器的设计方法；（三）控制规则的简便算法．     

分布参数控制系统逼近能达集对非线性扰动的不变性

一、引言非线性分布参数控制系统的能控性问题,在近二十年的研究中已经有了很多结果,但由于该问题难度较大,因而所得结论还比较零散,如,文[2,4,5,6]分别讨论了各类非线性分布参数控制系统的能控性.本文将在以上工作的基础上进一步讨论线性分布参数控制系统的逼近能达集对非线性扰动的不变性.对非线性扰动,我们给出了较弱的限制条件,由此可以得到一类非线性系统的逼近能控性,所得结论推广了很多已知的结果.     

弹性结构有限元控制系统

本文讨论了经有限元方法处理后的弹性结构系统的可控、可观测、镇定等问题.所得的结论与用分布参量系统模型所得的结论一致,但却便于用计算机计算且方法简单.在一、中研究了系统的可控与可观测的问题,给出了易于用计算机判别的条件.在二、中对于采用线性反馈镇定弹性体的问题进行了仔细的讨论,指出对弹性结构系统而言,若系统完全可控仅用位移反馈可以任意配置振动频率但却无法镇定系统,而仅用速度反馈虽可以进行镇定但镇定能力是有限的,对于在系统运动方程中包含刚体运动成分的情形也作了研究.在三、中对梁的控制问题用有限元进行了处理,指出直梁作为一个系统可以分解为拉压、扭转和两个方向弯曲这四个互不关联的子系统,它们的可控与可观测问题可以分别进行讨论.最后对折线型刚架的可控与可观测的问题也作了探讨.     

弹性振动点观测反馈控制古典解的存在性

本文运用有界线性算子的积分半群理论证明弹性振动点观测反馈控制方程古典解的存在性     

Controllability of impulsive neutral functional evolution integrodifferential systems with infinite delay

In this paper we establish sufficient conditions for the approximate controllability of impulsive neutral functional evolution integrodifferential systems in Hilbert spaces. Also we study the exact controllability of the same system. The conditions are obtained by using Schauder’s fixed point theorem when the operator is compact and the Banach fixed point theorem when the operator is not compact. The results are obtained by using the evolution operators.     

Pathological asymptotic behavior of control systems in Banach space

New phenomena arising when a linear dynamical system is defined on an infinite dimensional Banach space, although negligible from an engineering standpoint when only a finite time-interval is considered, become crucial when the asymptotic (feedback) behavior of the system is of interest. Pathologies with respect to the correspondent finite dimensional case are displayed even when the operator acting on the state is bounded.In particular, although in such case, the classical controllability and observability theory admits a natural generalization to infinite dimensions, the finite dimensional relationships between controllability and stabilizability fails. A few examples are given of systems that are approximately controllable and yet are not stabilizable: Moreover, such examples are drawn from a class of systems that can never be exactly controllable. The analysis is carried out using the perturbation theory of the spectrum. Another new feature of the infinite dimensionality of the state space is that even if the spectrum of an operator has the max of its real part equal to 0, yet the associated homogeneous differential equation may be globally asymptotically stable: Its consequence on stabilizability is also examined.     

Controllability and observability of coordinated linear systems

This paper develops concepts of controllability and observability for the class of coordinated linear systems, a special class of linear hierarchical systems with a top-to-bottom information structure. The usual concepts of reachability and indistinguishability for linear systems are refined, taking into account the decentralized nature of coordinated linear systems. The corresponding controllability and observability decompositions are derived, and several concepts of controllability and observability for coordinated linear systems are introduced and discussed. These results are then combined to a definition and characterization of stabilizability via dynamic measurement feedback for this class of systems.     

Modal analysis and control of a rotating Euler-Bernoulli beam part I: Control system analysis and controller design

Control of the vibration modes become critical when one wants to push the state of the art with faster, lighter, and more accurate flexible link. There are three steps which are necessary for the control of the flexible link. First, a good design based model of the plant must exist. Second, a good controller which is also realizable must be designed. Third, input to the controller must be constructed using knowledge of the system dynamic response. In this paper, involving a complete control strategy, pertaining to design based model, control, and dealing with the shaping of system input is presented. In Part I, a single-input single-output transcendental transfer function, pole-zero pattern, controllability, observability, and system type for distributed parameter system is illustrated by application to feedback control of an Euler-Bernoulli beam. The eigenfunctions, orthogonality condition, and mode summation method have been investigated in order to get the system analytical solution. A new control scheme, which depends on the pole-zero plot of the infinite-dimensional system and uses a realizable actuator and sensor without involving truncation of the higher-frequency modes, shows that good stability, robustness, and efficient tracking property can be achieved by moving all the poles of the corresponding closed-loop system further into the left half-plane.     

分布参数系统能控能观性问题的统一处理及应用

本文的主要目的是介绍一个统一的处理分布参数系统能控能观性问题的方法,并给出该方法在分布参数控制理论中的应用。为此,本文将从一类“类抛物” 偏微分算子（即没有椭圆性条件）的带权恒等式出发,给出所有已知的关于抛物型方程、双曲型方程、Schrödinger 方程和板方程的基于整体Carleman 估计的能控能观性结果。同时,基于该带权的恒等式,本文还给出它在双曲型系统的稳定性问题和在拟线性复Ginzburg-Landau 方程能控能观性等问题中的应用。     

Weighted Clément operator and application to the finite element discretization of the axisymmetric Stokes problem

We consider the Stokes problem in an axisymmetric three-dimensional domain with data which are axisymmetric and have angular component equal to zero. We observe that the solution is also axisymmetric and the velocity has also zero angular component, hence the solution satisfies a system of equations in the meridian domain. The weak three-dimensional problem reduces to a two-dimensional one with weighted integrals. The latter is discretized by Taylor–Hood type finite elements. A weighted Clément operator is defined and approximation results are proved. This operator is then used to derive the discrete inf–sup condition and optimal a priori error estimates.