解耦系统的特征结构配置

本文讨论线性时不变系统分~Ax+Bu,y~Cx,(1)在状态反馈及输人(非异)变换 u一犬x+G下,使闭环系统实现解耦且具有特定的结构配置问题.为此,总假设:系统(1)完全能控,x∈R~n,u∈R~r,y∈R~p,B,C 满秩,r=p.解耦问题早已有了一系列很好的结果.特别地,我们用[6]中的结果表述如下:设系统(1)的传递函数阵为     

线性奇异系统的解耦问题

本文讨论在状态反馈下的线性奇异系统的解耦问题，利用奇异系统的受限等价变换，给出了输出，输入维数相同的方线性奇异系统解耦问题有解的充分必要条件。     

广义控制系统状态观测器的结构

在广义控制系统的设计中,经常会遇到状态反馈问题.如极点配置和二次性能指标的最优控制都是状态反馈.可是在实际系统中,直接量测的是输出,而状态通常不能直接量测.从而知道状态反馈是物理上不能实现的.已知在正常系统中,解决这一问题的方法是重构状态——即通过一个被称为状态观测器的动态系统来实现它.因此对广义系统亦可期望通过状态观测器来获得状态反馈中的状态.文献[1]曾为广义系统具体设计了     

带控制器的弹性振动系统的能观性、能控性

<正> 在工作[1]中提出了带有控制迴路的分布参数反馈系统的模型.在工作[2]中讨论了以弹性樑的角速度、角度和线加速度作反馈信号输入到控制器,由控制器的输出端输出信号到舵的执行机构以实现反馈控制弹性振型的镇定问题.那里用的是线性算子的谱扰动方法.在[3]中讨论了不带控制器的弹性振动系统的能观测性和能控性问题,得到了能观测、能控的必要充分条件.在现代控制理论中,一个系统是否能控、能观测,无论在实际工     

非线性解耦问题的解及其唯一性

一、引言控制系统的反馈解耦问题已有很多研究,对于非线性系统,最先开始的研究是文[1]和[2].它们推广了单对单解耦问题著名的 Falb-Wolovich 条件.具有开拓性的研究是文[3]和[4].在获奖文[4]中,Isidori 等首次给出了非线性解耦问题的几何刻划.之后有更多、更进一步的研究.关于解耦问题的历史和发展,请读者参阅文献[8]和[9].近年来,解耦问题的研究兴趣还包括有动态反馈和奇异反馈设计.     

特征结构配置的多项式阵法

在多变量线性控制系统的设计中，为了使闭环系统具有更好的性能，提出了闭环系统的特征结构配置问题.即fll用状态反馈、输出反情或设计动杰补偿器.佑闭环索统的极点     

奇异系统的干扰解耦

本文针对线性的不变奇异系统，讨论了利用一般状态反馈及前馈控制的组合来达到其干扰解耦的条件．文中构造性地给出了这一问题可解的充分必要条件．     

关于非线性控制系统的线性化问题

本文首先研究了一般形式的非线性控制系统,得到了可以用状态反馈线性化时应具有的形式,即系统方程与控制规律一般条件下都应是对控制变量是线性的。然后研究了用状态变换进行线性化的问题,得到了变换应满足的条件。最后讨论了同时用状态变换与反馈变换对非线性控制系统进行线性化以及综合问题。     

线性系统稳定性与最优性的关系(Ⅱ)

我们在[1]中提出并讨论了与R.E.Kalman的最优控制反问题不同的另一类线性最优控制的反问题:任给一渐近稳定的定常线性系统和一个非负二次型性能指标,问是否可以从该稳定系统中分解出一个状态反馈,使得这个状态反馈就是给定指标下的最优控制。本文将上述问题加以推广,对线性离散系统和线性时变系统得出了相应的结论,进而得出[1]中提出的渐近稳定系统和最优系统之间的对应关系是一切线性系统的内在特征。     

输出反馈二次型最优的可解性问题

本文研究了用输出反馈实现二次型最优控制的问题,指出任何最优输出反馈都是对应最优状态反馈的衍生解和在一般情况下最优输出反馈所满足的线性矩阵方程是不可解的.并讨论了输出矩阵含有待定参数的情形,给出了最优输出反馈存在的必要条件,对于单输入系统证明了该条件几乎是充分的.     

奇异系统的微分和比例输出反馈正则化

奇异系统的微分和比例输出反馈正则化储德林（清华大学应用数学系）ＲＥＧＵＬＡＲＩＺＡＴＩＯＮＯＦＳＩＮＧＵＬＡＲＳＹＳＴＥＭＳＢＹＤＥＲＩＶＡＴＩＶＥＡＮＤＰＲＯＰＯＲＴＩＯＮＡＬＯＵＴＰＵＴＦＥＥＤＢＡＣＫ￥ＣｈｕＤｅ－ｌｉｎ（ＴｓｉｎｇｈｕａＵｎｉ...     

线性系统的输出反馈特征结构配置——具有不可控不可观模态的情形

本文考虑具有不可控不可观模态的线性系统的输出反馈特征结构配置问题。根据文中给出的矩阵方程AV＋BW＝VF的一种显式参数解，得到了线性系统的输出反馈特征结构配置的一种参数化方法，本文没有对系统附加能控能观条件，在[AB]能控的条件下，本文得到的矩阵方程的解是文[5]中定理2的结果，在[AB]能控且[AC]能观的条件下，本文得到的输出反馈特征结构配置方法是文[6]在系统为定常时算法Ⅱ的结果。     

Backstepping-based output regulation for systems with infinite-dimensional actuator and sensor dynamics

The output regulation problem is solved for an ODE plant driven by a parabolic actuator with spatially varying coefficients. Applying the backstepping transformation to the actuator allows the solution of the regulator equations in closed-form and thus the formulation of the solvability condition. An output feedback regulator is obtained by designing a disturbance observer using delayed measurement and a reference observer that both achieve finite-time convergence. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类不确定非线性系统的适应H-infinity控制

主要讨论了一类具有不确定参数的非线性系统的通过适应输出反馈达到干扰衰减的问题．通过构造降维观测器,利用Backstepping方法设计输出反馈控制器,使闭环系统具有不确定参数的标准的增益问题可解,并使系统达到内稳定．     

Reduced order controllers for distributed parameter systems: LQG balanced truncation and an adaptive approach

In this paper, two methods are reviewed and compared for designing reduced order controllers for distributed parameter systems. The first involves a reduction method known as LQG balanced truncation followed by MinMax control design and relies on the theory and properties of the distributed parameter system. The second is a neural network based adaptive output feedback synthesis approach, designed for the large scale discretized system and depends upon the relative degree of the regulated outputs. Both methods are applied to a problem concerning control of vibrations in a nonlinear structure with a bounded disturbance.     

Output tracking for an Euler–Bernoulli beam equation with moment boundary control and shear boundary disturbance

This paper is concerned with performance output tracking for an Euler–Bernoulli beam equation with moment boundary control and shear boundary disturbance. An infinite-dimensional disturbance estimator is designed to estimate the total disturbance. By compensating the total disturbance, a servomechanism corresponding to the reference signal and servomechanism-based output feedback control law are designed. It is proved that under such control law, the performance output tracks exponentially the reference signal and the involved states of closed-loop system are bounded. The most important contribution is to deal with the shear boundary term stemmed from the error system between the disturbance estimator and the original system. The admissibility does not hold for such shear boundary term, while the corresponding boundary terms in the existing literature was proved to be admissible. Two key steps are presented to cope with such problem: First, the semigroup generation and exponential stability for a coupled beam system are verified by Riesz basis approach; second, the admissibility of a control operator for semigroup governed by such coupled beam system is proved. Moreover, Sobolev embedding theorem is introduced to simplify the proof of the boundedness of the closed-loop systems with respect to the available literature. Some numerical simulations are presented to illustrate the effectiveness.     

Synthesis of multivariable regulators: The internal model principle

For the multivariable control system described by \(\dot x = Ax + Bu,y = Cx,z = Dx\) (wherey is the measured output andz the output to be regulated) conditions are given for the existence of a controller which preserves output regulation and loop stability, in the presence of small parameter variations in controller and plant. Under mild conditions, such a “strong” synthesis is shown to exist if and only if the regulator problem with internal stability (RPIS) is well-posed. Synthesis is achieved by means of a feedback configuration which in general incorporates an invariant, and suitably redundant, copy of the dynamic model adopted for the exogenous disturbance and reference signals which the system is required to process.     

The internal model principle for linear multivariable regulators

Necessary structural criteria are obtained for linear multivariable regulators which retain loop stability and output regulation in the presence of small perturbations, of specified types, in system parameters. It is shown that structural stability thus defined requires feedback of the regulated variable, together with a suitably reduplicated model, internal to the feedback loop, of the dynamic structure of the exogenous reference and disturbance signals which the regulator is required to process. Necessity of these structural features constitutes the internal model principle.This research was partially supported by the National Research Council of Canada, Grant No. A-7399.     

Output feedback stabilization for a class of nonlinear time-evolution systems

A variety of problems in nonlinear time-evolution systems such as communication networks, computer networks, manufacturing, traffic management, etc., can be modelled as min–max-plus systems in which operations of min, max and addition appear simultaneously. Systems with only maximum (or minimum) constraints can be modelled as max-plus system and handled by max-plus algebra which changes the original nonlinear system in the traditional sense into linear system in this framework. Min-max-plus systems are extensions of max-plus systems and nonlinear even in the max-plus algebra view. Output feedback stabilization for min–max-plus systems with min–max-plus inputs and max-plus outputs is considered in this paper. Max-plus projection representation for the closed-loop system with min–max-plus output feedback is introduced and the formula to calculate the cycle time is presented. Stabilization of reachable systems with at least one observable state and a further result for reachable and observable systems are worked out, during which max-plus output feedbacks are used to stabilize the systems. The method based on the max-plus algebra is constructive in nature.     

Resource-saving infinite-horizon tracking under uncertain input

A feedback controller for approximate tracking a prescribed trajectory of an inaccurately observed dynamical system effected by uncertain non-observable input disturbances over an infinite time interval is constructed. The controller is “resource-saving” in a sense that control resources spent for approximate tracking do not exceed (with some small gaps) those needed for exact tracking in an “ideal” situation where the current values of the input disturbance are fully observable.