課程資訊
課程名稱
 數理控制論二
Methemetical Control Theory(Ⅱ) 
開課學期
 102-2 
授課對象
 理學院  數學研究所  
授課教師
 容志輝 
課號
 MATH5429 
課程識別碼
 221 U6210 
班次
  
學分
 3 
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101 
備註
 總人數上限：30人 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/1022math_ctrl_theory 
課程簡介影片
 
核心能力關聯
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課程大綱
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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 spring semester will cover what constitutes the common core of robust control theory, namely H2 and H-infinity optimal control theory. Both linear and nonlinear systems are discussed. Some fundamental nonlinear geometric control theory will be covered too, including feedback linearization, zero dynamics, enter manifold, and output regulation problem 
課程要求
 It is assumed that students in the class to are familiar with Mathematical Control Theory I.
NO KNOWLEDGE OF DIFFERENTIAL GEOMETRY IS NEEDED! 
預期每週課後學習時數
  
Office Hours
 另約時間 
指定閱讀
 Lecture Note.  
參考書目
 References：
1)Sontag, Mathematical Control Theory, Second Edition, Springer-Verlag, 1998.
2)Trentelman, Stoorvogel and Hautus, Control Theory for Linear Systems, Springer, 2001.
3)Zhou, Doyle, and Glover, Robust and Optimal Control, Prentice-Hall, 1996.
4) Isidori: Nonlinear Control Systems, Vol 1, Springer, 3rd Edition.
5) 期刊文獻。 
評量方式
(僅供參考)
    
課程進度
週次
日期
單元主題
第1週
 2/21  Linear-Quadratic (LQ) optimal control 
第2週
 2/28  H2 optimal control theory 
第3週
 3/07  Standard H-infinity control problem and bounded real lemma 
第4週
 3/14  H-infinity state feedback control 
第5週
 3/21  H-infinty output feedback control  
第6週
 3/28  Doubly Besout identity in RH^\infty and Youla parameterization of all stabilizing controllers 
第7週
 4/04  Parameterization of all H-infinity output feedback controllers 
第8週
 4/11  Nash Game and Mixed H2/H-infinity control(optional) 
第9週
 4/18  H-infinity controller reduction 
第10週
 4/25  Controllability and observability gramians and balanced realization  
第11週
 5/02  Hankel operator and balanced truncation 
第12週
 5/09  Lyapunov stability theory for nonlinear systems, L2 gain analysis 
第13週
 5/16  Differential game theory, Hamiltonian-Jacobi nonlinear PDE, nonlinear H-infinity state feedback control 
第14週
 5/23  Nonlinear H-infinity output feedback control 
第15週
 5/30  Feedback Linearization theory 
第16週
 6/06  Zero Dynamics and center manifold theory 
第17週
 6/13  Output regulation for nonlinear systems