基于隐函数方法的离散双线性系统临近可控性研究

项目名称： 基于隐函数方法的离散双线性系统临近可控性研究

项目编号： No.61203231

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 自动化学科

项目作者： 铁林

作者单位： 北京航空航天大学

项目金额： 25万元

中文摘要： 一非线性系统，若关于状态和控制分别、但不同时是线性的，则称为双线性系统。本课题以离散双线性系统为对象，针对临近可控性问题展开研究。开展此项研究是基于以下三方面。第一，双线性系统是一类特殊的非线性系统，广泛存在于现实世界中，如工程、经济、生物等领域，是最接近于线性系统的非线性系统。用双线性系统逼近非线性系统具有比线性逼近更准确、精确的效果。第二，随着计算机技术的普及，离散控制系统的重要性日益突出，其分析与综合已成为现代控制理论的重要组成部分。第三，可控性是控制科学的基本概念，并在数学控制理论中发挥重要作用。临近可控性则是近年新提出、包含了可控性的更广泛的概念，更全面地描述了系统的性质。本课题采用一种隐函数方法，重点研究并解决离散双线性系统的临近可控性问题，给出判据。具体研究内容包括自身可控性、局部可控性、连通性、临近可控性、镇定性等问题。预期研究成果将对双线性系统理论的发展具有重要推动意义。

中文关键词： 双线性系统；离散系统；可控性；临近可控性；临近可控子空间

英文摘要： A nonlinear system is called a bilinear one if it is linear in state and linear in control, but not jointly linear in both. This work investigates near-controllability of discrete-time bilinear systems. The purpose of this work is based on the following three aspects. Firstly, bilinear systems are a special class of nonlinear systems, which exist widely in the real world such as engineering、economic、biology, etc. Among nonlinear systems, bilinear systems are the most close to linear systems. Furthermore, bilinear systems have well approximation properties. It is in general more accurate to use a bilinear model to represent the dynamics of a nonlinear system than to use a linear model. Secondly, due to the wide applications of computer technology, the importance of discrete-time control systems is well realized nowadays. The analysis and synthesis of discrete-time control systems has become an important part of modern control theory. Thirdly, controllability is one of the fundamental concepts in control subjects and has played an essential role in the development of mathematical control theory. The notion of near-controllability was introduced recently, which not only contains the notion of controllability, but also can better characterize the properties of control systems. This work will apply an implicit funct

英文关键词： Bilinear Systems；Discrete-time Systems；Controllability；Near-controllability；Nearly-controllable Subspaces