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摘要状态变量始终为非负的系统称之为非负系统。线性系统被认为是系统和控制学科领域中最基本的研究对象。在控制理论中，可控性和可观测性是最经典的理论。可控性是控制函数对系统运动行为的影响能力。可达性问题是把现代计算机技术与控制理论相结合的产物。对于线性系统来说，可控性与可达性是等价的。对于线性系统的可达性的研究具有很重要的意义。67253
本文主要对线性系统可达集的范围进行研究。在经典的控制理论中，控制函数只要求是一个可测的函数。本文由二阶非负系统入手，给出了系统的可达集及其描述方法。
本文的主要工作有以下几个部分：
1) 分别给出了当非负系统无控制项u(t)，即自由非负线性系统 和当控制函数u(t)有界，非负系统 ， 时的可达集的估计及边界，并表示出系统状态x(t)的所有点，对系统可达区域进行椭圆估计。
2) 证明控制函数为凸集时可达集的凸性。
3) 说明控制函数为多面体时可达集也为多面体并给出可达集具体表达式。
4) 讨论线性系统二次型最佳控制。
毕业论文关键词：连续线性系统； 非负系统； 可控性； 凸性； 可达集范围。
毕业设计说明书（论文）外文摘要
Title Estimation of the reachable set of the non-negative system
Abstract
It is called non-negative system if all its state variables are non-negative. The linear system is considered to be the most basic objects of study in the control system. Controllability and observability are the classical theories in control system theories. Controllability is the ability that the control function influences on the systemic behavior and reachability problem is combination product of the modern computer technology and control theory. They are equivalent for linear systems. Consequently, research on reachability plays a pivotal role in the study of controllability of the linear system.
In this paper, we mainly start with investigation of the second-order non-negative system to get the reachable set of all system states and find a desirable approach to bound the set.
The thesis consists of four major parts as follows:
1) Estimations of the reachable set and its boundary are provided respectively for non-negative systems without control signal or with a bounded control u(t). All points of the system state x(t) are illustrated and ellipse estimation of the reachable set is given.
2) Proof of the convexity of the reachable set is given when the control function is convex.
3) The conclusion that the reachable set is polyhedra when the control function is polyhedra and the concrete expression of the reachable set are given.
4) The optimal control of linear quadratic is discussed.
Keywords: continuous-time linear systems; controllability; bounded control; convexity; reachable set.
目录
1 绪论 1
1.1 历史回顾和研究现状 1
1.2 本文的问题描述和工作安排 2
2 预备知识 2
2.1 可达性问题 2
2.1.1 可达集相关概念 2
2.1.2 可达集表示方法研究 3
2.2 线性系统的相关概念和理论