本講義では, 計測・制御工学を学んでいく上で必須となる数学的ツールを身に付けることを目的として,複素関数論, ラプラス変換, フーリエ変換の基礎を中心に解説する. |
Lecture# | Dates |
Topics |
Exam/Exercise Problems |
Handouts |
|
1 | 4月16日 | 複素数と複素関数 | exercise1.pdf | ||
2 | 4月23日 | 複素関数の微分 | exercise2.pdf | ||
3 | 4月30日 | 複素関数の積分 | exercise3.pdf | ||
4 |
5月 7日 | ローラン展開と留数 | exercise4.pdf | ||
5 | 5月14日 | 留数定理と定積分 | exercise5.pdf | ||
6 | 5月21日 | 等角写像 | exercise6.pdf | ||
7 | 6月 4日 | 複素関数まとめ | exercise7.pdf | ||
8 | 6月11日 | Mid-Term Exam | MT_exam.pdf | ||
9 | 6月18日 | ラプラス変換の基礎 | exercise8.pdf | ||
10 | 6月25日 | ラプラス変換の性質 | |||
11 | 7月 2日 | ラプラス変換まとめ | exercise9.pdf | ||
12 | 7月 9日 | フーリエ級数 | exercise10.pdf | ||
13 | 7月16日 | フーリエ変換 | exercise11.pdf | ||
14 | 7月23日 | フーリエ積分 | |||
7月30日 | Final Exam | Final_exam.pdf |
1. | Advanced Engineering Mathematics, | Erwin Kreyszig, Wiley |
1. | 応用解析学入門 白井宏著 コロナ社 |
Linear Systems and Control (Fall/Winter 2009)
Introduction to linear systems theory and feedback control. This course provides a foundation of modern control theory and also covers several advanced topics in linear dynamical systems. |
Lecture# |
Date |
Topics |
Handouts |
|
1 |
Oct. 2 |
Linear algebra and coordinate
transformation |
||
2 |
Oct. 9 |
Controllability and observability |
||
3 |
Oct. 16 |
Realization of transfer functions |
||
4 |
Oct. 30 |
Lyapunov stability theory and Lyapunov
functions |
||
5 |
Nov. 6 |
Positive real and bounded real
theory |
||
6 |
Nov. 13 |
Linear feedback control |
||
Dec. 20 |
FINAL EXAM |
Nonlinear and Adaptive Control (Fall/Winter 2009)
Theory and application of nonlinear and adaptive control systems. Discussed are methods of on-line parameter identification and adaptive control for nonlinear systems with uncertain parameters. To this end, Lyapunov stability theory and Lyapunov functions for general nonlinear systems are examined in the first half of the course. |
Projected course schedule:
Lecture# |
Date |
Topics |
Handouts |
|
1 |
Nov. 27 |
Nonlinear dynamical system theory (existence and uniqueness of solution) |
||
2 |
Dec. 4 |
Nonlinear dynamical system theory (Lyapunov's stability theory) |
||
3 |
Jan. 8 |
Nonlinear dynamical system theory (dissipativity theory) |
||
4 |
Jan. 22 |
Normal form representation |
||
5 |
Jan. 29 |
Nonlinear adaptive control (1) |
||
6 |
Feb. 5 |
Nonlinear adaptive control (2) |
||
Feb. 12 |
FINAL EXAM | Exam2009 |
References: