ECE1647F Introduction to Nonlinear Systems (Last updated October 24, 2020)

Teaching Staff

Prof. M.E. Broucke GB434A Instructor broucke at control.utoronto.ca
Ahmad Abdel Gawad GB348 TA ahmad dot abdelgawad at mail.utoronto.ca


Lecture Schedule

Lectures will be posted online each week.


References

Course notes will be distributed to registered students. In addition the following references may be helpful.



Course Outline

Here is a nominal timetable of lecture topics. This schedule may be updated as the semester progresses.

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, Poincare-Bendixson 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, Hartman-Grobman Theorem  
    14 Lyapunov stability theory  
8 Nov 2 15 Barbashin-Krasovksii 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


Homework

Homework Chapter Problems Due Date
1 Appendix A A.13, A.14, A.15, A.16, A.17, A.18, A.22, A.24, A.25 October 2
2 Chapter 1 1.5, 1.10, 1.11, 1.13, 1.15 (parts 2, 6), 1.16 October 19
3 Chapter 2 2.2, 2.3, 2.4, 2.5, 2.8, 2.9 November 2
4 Chapter 3 3.8, 3.9, 3.10, 3.11 November 30


Grading

Homework 30%
Midterm 30%
Final Project 40%