Week 
Date 
Lecture 
Topics 
Due Dates 
1 
Sept 14 
1 
Introduction: ODEs, vector fields, dynamical systems 



2 
Mathematical preliminaries 

2 
Sept 21 
3 
Mathematical preliminaries 



4 
Existence and uniqueness of solutions 

3 
Sept 28 
5 
Finite escape time, continuity w.r.t. ic's, comparison lemma 
Homework 1 


6 
Invariant sets, Special Nagumo theorems 

4 
Oct 5 
7 
Nagumo theorem 



8 
Limit sets, PoincareBendixson theorem 

5 
Oct 12 
9 
Application: gait control of a walking robot 



10 
Stability of periodic orbits 

6 
Oct 19 
11 
Stability of periodic orbits 
Homework 2 


12 
Application: gait control of a walking robot
 
7 
Oct 26 
13 
Linearization, HartmanGrobman Theorem 



14 
Lyapunov stability theory 

8 
Nov 2 
15 
BarbashinKrasovksii Theorem, Converse theorems 
Homework 3 


16 
LaSalle Invariance Principle 


Nov 9 

Fall Break 
Project Proposal 
9 
Nov 16 
17 
Barbalat's Lemma 
Midterm Exam 


18 
Feedback linearization 

10 
Nov 23 
19 
Feedback linearization 



20 
Feedback linearization 

11 
Nov 30 
21 
Feedback linearization 
Homework 4 


22 
Adaptive control 

13 
Dec 14 

Adaptive control 
Final Project 