【作者】 张雪峰；

【导师】 张庆灵；

【作者基本信息】 东北大学 ， 控制理论与控制工程， 2010， 博士

【摘要】 线时变周期(LTVP)系统存在于许多实际工程技术领域,如弹性力系统、参数共振、质子加速器、天体力学、激光物理、卫星姿态控制、直升飞机传动系统、生态系统和经济系统中周期环境的竞争平衡等。线时变周期系统是一类重要而又研究成果较少的系统。粗糙集(Rough Set)理论是一种刻划不完整性、不确定性和不相容的数学工具,可以从数据本身中发现隐含的知识,解释潜在的规律。粗糙集理论为专家控制、智能控制提供了重要的理论基础。本文借鉴线性系统理论和现代鲁棒控制理论的思想,利用粗糙集理论方法,研究了LTVP系统能控性、能观性、渐近稳定性、Riccati稳定性分析问题,考虑了粗糙控制与网络控制问题,主要工作概括如下：1.给出和改进了若干粗糙集数据处理的有效算法,提出对象编码后再扫描的方法,降低了复杂度,给出利用属性重要度进行属性约简、基于层次分析和简单相异矩阵属性约简、变精度粗糙集属性约简、区间数系统属性约简的算法。2.利用MATLAB作为开发语言,编写了粗糙集数据处理方法的仿真工具箱软件程序,包括启发式属性约简,变精度属性约简,相异矩阵的属性约简,区间数属性约简,求上下近似,求核,规则生成等的程序,设计了图形用户界而。填补MATLAB软件粗糙集工具方面的空白。3.给出了线性时变周期(LTVP)系统能控性的两个新的必要条件,该方法无须利用系统的状态转移矩阵,方便可行。讨论了时变广义系统的能控性,举例指出《IET, Control Theory and Application》上关于线性时变周期系统能控性的一个错误结论。利用对偶原理,所有能控性的结果都扩展到了能观性对应的结果。4.解决了Riccati稳定的充分必要条件,此方法只依赖于系统本身的结构,不用依赖求解LMIs的可行解。得到了基于LMIs方法的LTVP系统Riccati稳定的充分条件,举例说明了线性定常系统系统的Riccati稳定在时延系统和鲁棒系统中的原因,设计了LTVP系统无记忆状态反馈控制器,鲁棒、H∞控制器,分析了LTVP时延系统稳定性。5.综述和总结粗糙控制的各种应用,介绍粗糙集在过程控制的模糊隶属函数求取及倒立摆系统应用的方法,进行了LTVP网络控制系统稳定性分析与控制器设计,讨论了广义正定与稳定性的关系,指正广义正定方面的一个误解。更多还原

【Abstract】 Linear time varying periodic (LTVP) systems can be found in many engineering technology field, such as flexible mechanics system, parameter resonator, proton ac-celerator, celestial mechanics, laser physics, satellite gesture control, helicopter drive system, ecosystem, economic system, period environment competition balance etc. Linear time varying periodic systems are a class of systems that are very important but have less research results. The rough set (RS) theory is a new mathematical tool to deal with imprecise, incomplete and inconsistent data. It can find hidden knowl-edge and explain latent rules from itself data. Rough set theory provides theory base for expert control and intelligence control. With the thought of linear system theory and modern robust control theory, and the method of rough set theory, the analy-sis of controllability, observability, asymptotic stability, Riccati stability and rough control, networked control of LTVP systems are considered. The main contents of the dissertation can be briefly described as follows:1. The effective algorithms of rough set data analysis are presented and im-proved. The method of coding and scanning objects is considered. The algorithm complex degree is reduced. The heuristic attribute reduction algorithm with at-tribute importance, based on discriminative matrix attribute reduction algorithm, hierarchic analysis attribute reduction algorithm, variable precision attribute reduc-tion algorithm and interval number attribute reduction algorithm are presented.2. By using MATLAB as the development language, the simulation tool box software of rough set data analysis is firstly programmed, including heueristic at-tribute reduction algorithm, disceraisility matrix attribute reduction algorithm, vari-able precision attribute reduction algorithm and interval number attribute reduction algorithm. The program of upper approximation, lover approximation realization equivalence relation, relatively attributes reduction, attribute core, etc. are ob-tained. The graphic user interface is designed. The deficiency of MATLAB software at rough set tool box aspect is filled up.3. The new necessary conditions of controllability of LTVP systems are ob-tained. The method has feasibility and is more convenient. It dose not need cal-culating the state transition matrix. The controllability of time varying descriptor systems is discussed. An error conclusion of controllability of LTVP systems in the journal of IET control theory and application is pointed out by an example. By duality, all the obtained results can be extended the corresponding observability results.4. The necessary and sufficient conditions of Riccati stability of linear time in-variant (LTI) systems are given. The method only depends on the system structure, without the calculation of LMIs feasibility. The necessary and sufficient conditions of Riccati stability of LTVP systems are provided. The applications of Riccati stability of LTI systems in time delay systems and robust control systems are demonstrated by two examples. The memoryless state feedback controller, robust controller and H∞controller of LTVP systems are designed. The stability of LTVP time delay systems is analyzed.5. Survey and summary of rough control and networked control systems are provided. The method of rough control and selection of fuzzy member function are introduced. The control and simulation of networked control inverted pendulum are discussed. The stability of LTVP networked control systems is analyzed and the controller of LTVP networked control systems is designed. The relation between generalized positive definite and stability is discussed. A mistake on generalized positive definite application is pointed out.更多还原