课程编号:S209G023
现代控制理论
学时:32 学分:2 开课时间:秋季授课单位:管理学院 任课教师:唐万生
一、课程内容简介
本课程是系统工程专业硕士研究生的学位课,其目的是使硕士生掌握现代控制理论的基础知识和处理问题的方法,为系统工程硕士生进一步学习后继的专业课和开展研究工作奠定基础.本课程分成如下两部分.
第一部分为线性系统分析与设计,包括控制系统的状态空间表述,状态方程的建立,线性系统的状态转移矩阵,线性系统的动态响应公式,线性系统传递函数的各种实现方法,线性定常系统的等价性,线性系统的能控性及判别条件,线性定常系统的能控子空间,线性定常系统的能控分解,线性系统的能观性及判别条件,线性定常系统的不能观子空间,线性定常系统的能观分解,对偶系统及能控与能观的对偶性,线性定常系统的结构分解,传递函数的最小实现及最小实现的唯一性,状态反馈控制与极点配置,线性定常系统可任意配置极点的充要条件及配置方法,线性定常系统的状态观测的设计方法.
第二部分为最优控制理论,包括最优控制的数学描述,泛函的变分,变分法,欧拉-拉格郎日方程,无约束最优控制问题,最优控制满足的必要条件,正则方程及各种边界条件,求解最优控制的方法,Pontryagin极大值原理及其应用,线性二次调节问题,离散时间系统的最优控制问题,动态规划方法及其应用等.
本课程采用多媒体课件授课,同时使用计算机完成相关的设计和计算.
Modern Control Theory
The primary purpose of this course is to introduce the fundamental knowledge and approach of modern control theory. It is used to enable the master students of systems engineering to develop study. It is assumed that the students taking the course had also taken, as a prerequisite, an undergraduate course in classical control theory and also were familiar with certain standard linear algebra as well as the theory of ordinary differential equations.
The course contains two major parts. The first of these outlines the basic theory of linear systems. It includes the following: The state space representation and the state equation of linear dynamical systems. The state transition matrix and the response formulation of linear systems are introduced. The methods of the passage from transfer function matrix to state space equations are given. The definition and some criteria of controllability for linear systems, and the controllable subspace are presented. The definition and some criteria of observability for linear systems, and the no-observable subspace are presented also. The dual theorem of controllable and observable for linear systems is introduced. The Kalman's structure decompounded method for linear systems is given. The method of minimal realization of transfer function matrix, and the uniqueness of minimal realization are provided. The state feedback control law and the poles placement are introduced. The sufficient and necessary condition of arbitrary to place the poles for linear systems is given. The design methods of state observer for linear systems are provided.

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