【作者】 刘梅；

【导师】 段广仁； 张焕水；

【作者基本信息】 哈尔滨工业大学 ， 控制理论与控制工程， 2006， 博士

【摘要】 时滞,既可能是物理现象固有的,也可以是有意识地引入到系统设计中,用来消除或降低时滞的影响。忽略时滞的存在,常常造成系统控制性能下降甚至系统不稳定。自上个世纪六十年代开始,时滞系统的控制逐渐成为控制理论研究的热点和难点。尽管人们已经取得了众多有关时滞系统控制问题的结果,往往都归结为一些较为复杂的问题,使得问题并没有得到根本的解决。对离散时滞系统,人们倾向于通过增广系统将时滞问题转化为无时滞问题。然而,当系统有多个时滞且时滞较大时,增广系统将会导致系统维数增加,计算量增大。连续系统的时滞问题通常用到无穷维算子的Riccati方程,这种算子方程既难于理解又不便应用。观测时滞可能是由系统的固有时滞特性引起的,而本文中观测方程中出现时滞则往往是由于用于观测的传感器在信号传输过程中导致的滞后系统。常见的观测时滞系统,如带有滞后的最优控制模型、投入产出模型、柔性机器人模型等。输入时滞产生的原因可能是在求取所需控制作用时,常需要时间对传感器数据进行过滤和处理,也可能是执行器需要一定的时间获得所需的控制作用。在许多工程领域,如飞行器控制和网络控制,都有输入时滞现象。本文研究了两个问题,观测时滞的H∞输出反馈控制问题与多输入时滞的跟踪控制问题,每个问题都分别考虑了离散与连续系统。本文的创新点为:第一、本文提出了一种基于Krein空间重组新息分析解决观测时滞H∞输出反馈控制问题的新方法。基于Krein空间理论将观测时滞的H∞输出反馈控制问题分解为一个线性不定二次调解(LQR)控制问题与一个时滞的H2估计问题。由于LQR问题的结果已知,利用重组观测技术将时滞的H2估计问题转化为无时滞的H2估计问题,从而可由Kalman滤波求解。第二、利用Krein空间重组新息分析方法,给出了单观测时滞H∞输出反馈控制问题与多观测时滞H∞输出反馈控制问题有解的充要条件,该条件易于用Matlab进行验证;给出了满足H∞性能指标的控制器的显式表达式(即解析解),该控制器由两个与系统同维的Riccati方程决定。第三、基于Krein空间理论,首次建立了多输入跟踪控制问题与一个平滑问题之间的对偶关系。多输入跟踪问题可以转化为Krein空间中一个倒向随机系统的最有问题,而该最优问题对偶与一个固定平滑问题。通过这种对偶关系,由平滑问题的增益矩阵即可给出最优跟踪控制器的显式表达式。Krein空更多还原

【Abstract】 Delays could arise as well from inherent physical phenomena and also couldbe intentionally introduced for some design consideration in order to eliminate orreduce the e?ect of time delay. As a source of degradation in control e?ciencyand instability of control system, delays can not be ignored. Thus, it has been anactive and complicated research area since the 1960’s. Although plenty of resultsabout time delay system control have been achieved, most of them are induced tosome di?cult problem and not solved in essence. For discrete-time systems withdelays, one might tend to consider augmenting the system and convert a delayproblem into a delay-free problem. While the augmentation approach generallyresults in higher state dimension and thus high computational cost, especiallythe systems under investigation involves multiple delays and the delays are large.For continuous-time systems, the delayed problems can in principle be treatedby the infinite-dimensional operator Riccati equations which are di?cult to beunderstood and implemented.The intrinsic time delayed properties of system may lead to measurementdelays, but the time delays in measurement equations of this thesis are alwaysresulted from the signal transmission processing of the sensors which is used toobserve. System with time delay in measurements arise in the optimal controlmodel with delays, input/output model and ?exible robot model. The time takenin the filtering and processing of the sensory data for the required control forcecalculation and the transmission of the control force to the actuator or the timetaken by the actuator to produce the required control force may result in inputdelays. System with input delay arise in many engineering fields such as aircraftcontrol and network control.In this thesis, we considered two problems which are discussed for discrete-time case and continuous-time case, respectively. One is measurement-feedbackH∞control for systems with delayed measurement(s), and the other one is thetracking control for systems with multiple input delays. The main contributionsof this thesis are listed as follows.First, we proposed a new method which solved the problems of measurement-feedback H∞control with delayed measurement(s) by re-organized innovationanalysis approach in Krein space. Based on Krein space theory, the problems更多还原