具有可列Markov跳变结构的随机乘积噪声系统的能观性、能检性及其在H2/H∞控制中的应用

项目名称： 具有可列Markov跳变结构的随机乘积噪声系统的能观性、能检性及其在H2/H∞控制中的应用

项目编号： No.61304074

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 侯婷

作者单位： 山东科技大学

项目金额： 24万元

中文摘要： Markov跳变系统能够很好地描述由随机突发现象引起的物理系统状态和参数的跳变特性，其理论与技术一直是控制领域的研究热点。然而现有成果普遍是基于Markov链的状态空间是有限集的假设得到的，鲜见可列无穷集情形，尤其在结构特性方面，尚未涉及能观性的研究，已提出的能检性概念均是出于理论推导的需要从数学角度引进的，无法体现系统本身的动力学性能。事实上，可列跳变系统的模型更具一般性，其性质与有限跳变情形存在本质差异。本课题拟首先从量测输出和状态二者之间的联系角度定义这类系统的精确能观（检）性，借助无穷维Banach空间中的算子谱理论建立相应的谱判据。进而探讨精确能观假设下广义代数Riccati方程的镇定解的性质；在精确能检条件下，证明系统稳定等价于广义Lyapunov方程的半正定解存在且惟一，并将上述结论应用于无穷时域H2/H∞控制器的设计中。最后研究转移概率信息部分未知时H2/H∞控制器的设计。

中文关键词： 可列无穷马尔可夫跳；乘积噪声；能检性；能观性；H2/H∞控制

英文摘要： Markov jump systems can be well used to capture the switching property of the state and parameters of physical plants caused by randomly abrupt phenomena. Therefore, the relevant theory and technique have long been hot topics in the field of control studies. While fruitful results have been contributed under the assumption that the underlying Markov chain takes values in a finite set, there is little progress concerning the countably infinite jump case in the available literature. Especially on the structural characteristics, the study of observability for countably infinite Markov jump systems remains untouched. Moreover, the existing notions of detectability are all introduced from the mathematical viewpoint due to the requirement of theoretical derivation, which can not reflect the dynamic behavior of real plants. In fact, the model of countably infinite jump systems is more general and its property is essentially different from that of the finite jump case. The first intention of this project is to properly define the concepts of exact observability and exact detectability for stochastic systems with countably jumping structures, according to the relationship between the measurement output and system state. Then, by use of the operator spectrum in an infinite dimensional Banach space, corresponding spectral

英文关键词： countably infinite Markov jump；multiplicative；detectability；observability；H2/H∞ control