課程大綱

課程資訊

課程名稱

數理控制論一
Methemetical Control Theory(Ⅰ)

開課學期

102-1

授課對象

理學院數學系

授課教師

容志輝

課號

MATH5428

課程識別碼

221 U6200

班次

學分

全/半年

半年

必/選修

選修

上課時間

星期五7,8,9(14:20~17:20)

上課地點

天數305

備註

總人數上限：30人

Ceiba 課程網頁

http://ceiba.ntu.edu.tw/1021math_ctrl_theory

課程簡介影片

核心能力關聯

本課程尚未建立核心能力關連

課程大綱

為確保您我的權利,請尊重智慧財產權及不得非法影印

課程概述

...Mathematical control theory is now a very active research field, sharing with some other areas of modern applied mathematics (such as quantum field, geometric mechanics and scientific computation etc.) and providing many challenges and possibilities of interactions with established areas of pure mathematics (such as algebraic geometry, differential and Riemannian geometry, real analysis, functional analysis, topology, Lie groups and Lie algebras, in addition to linear algebra, complex variables, ODE, and PDE etc.). In this introductory course, we shall introduce the basic concepts and fundamental results of mathematical control theory, with special emphasis on the various geometric subspaces of the state space and related mathematical control problems.

課程目標

This introductory course in the fall semester will cover what constitutes the common core of mathematical control theory: The algebraic theory of linear systems, including reachability, observability and minimality; stability via Lyapunov; state feedback and optimal control, observers and dynamic output feedback, and so on.

課程要求

The minimal mathematical background in the first semester that is required of the students is a working knowledge of linear algebra and differential equations, no need to have any engineering background.

預期每週課後學習時數

Office Hours

另約時間

指定閱讀

待補

參考書目

. ＊Reference material ( textbook(s) )：
1)Sontag, Mathematical Control Theory, Second Edition, Springer-Verlag, 1998.
2)Trentelman, Stoorvogel and Hautus, Control Theory for Linear Systems, Springer, 2001.
3)Wonham, Linear Multivariable control: A Geometric Approach.3rd Edition, Springer-Verlag, 1985.
4)Zhou, Doyle, and Glover, Robust and Optimal Control, Prentice-Hall, 1996.
5) 容志輝著，基本線性系統理論，全華書局，2003。
6) 期刊文獻。

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	上課情形	10%
2.	作業	90%

課程進度

週次	日期	單元主題
第1週	9/13	Introduction, Exponential of Square Matrices, Solution of Dynamical Equations.
第2週	9/20	中秋節彈性放假
第3週	9/27	Invariant and (Largest) Weakly Invariant Subspaces,
第4週	10/04	Observability, Weak Observability, Strong Observability, Reachability, Controllability, Quotient Spaces, Quotient Maps.
第5週	10/11	Quotient Systems, Kalman Decomposition.
第6週	10/18	Minimal Realization, State Feedback and Pole Placement Problem.
第7週	10/25	Stability, Stabilizability.
第8週	11/01	State Estimation, Separation Principle, Detectability, Well-Posedness.
第9週	11/08	Feedback Stabilization Problems, Smith Form, Smith-McMillan Form, Poles and Zeros of a Transfer Function.
第10週	11/15	校慶停課
第11週	11/22	Greatest Common Right and Left Divisors, Coprimeness, Bezout Identity.
第12週	11/29	Right and Left Coprime Factorization of a Transfer Function, Doubly Coprime Factorization.
第13週	12/06	Transimission Zeros and Poles.
第14週	12/13	System Matrix, Invariant Zeros, Input-Decoupling Zeros, Output-Decoupling Zeros, Input-Output Decoupling Zeros, Nyquist Stability Theorem.
第15週	12/20	Tensor Product, Sylvester Equation, Lyapunov Stability Theorem, Controllability and Observability Gramians.
第16週	12/27	Algebraic Riccati Equations.
第17週	1/03	Disturbance Decoupling Problems, Output Regulation Problems.