COM-502 / 4 crédits

Enseignant: Thiran Patrick

Langue: Anglais


Summary

Linear and nonlinear dynamical systems are found in all fields of science and engineering. After a short review of linear system theory, the class will explain and develop the main tools for the qualitative analysis of nonlinear systems, both in discrete-time and continuous-time.

Content

Keywords

Dynamical Systems, Attractors, Equilibrium point, Limit Cycles, Stability, Lyapunov Functions, Bifurcations, Lyapunov exponents.

Learning Prerequisites

Required courses

  • Linear algebra (MATH 111 or equivalent).
  • Analysis I, II, III (MATH 101, 106, 203 or equivalent).
  • Circuits & Systems II (EE 205 or equivalent) or a Systems & Signals class (MICRO 310/311 or equivalent).

Recommended courses

  • A first-year Probabilty class, such as MATH-232, MATH-231, MATH-234(b), MATH-234(c), or equivalent.
  • Analysis IV (MATH 207 or equivalent)

Important concepts to start the course

  • Linear Algebra (vector spaces, matrix operations, including inversion and eigendecomposition).
  • Calculus (linear ordinary differential equations; Fourier, Laplace and z-Transforms).
  • Basic notions of topology.
  • Basic notions of probability.

Learning Outcomes

By the end of the course, the student must be able to:

  • Analyze a linear or nonlinear dynamical system.
  • Anticipate the asymptotic behavior of a dynamical system.
  • Assess / Evaluate the stability of a dynamical system.
  • Identify the type of solutions of a dynamical sytem.

Teaching methods

  • Lectures (blackboard), 2h per week
  • Exercise session, 1h per week.

Expected student activities

Exercises in class and at home (paper and pencil, and Matlab)

Assessment methods

  1. Mid-term : cannot be given this year.
  2. Final exam 100%

Supervision

Office hours Yes
Assistants Yes
Forum Yes

Resources

Bibliography

Course notes; textbooks given as reference on the moodle page of the course.

Notes/Handbook

Course notes, exercises and solutions provided on the moodle page of the course.

Moodle Link

Prerequisite for

Classes using methods from dynamical systems.

Dans les plans d'études

  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Dynamical system theory for engineers
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 1 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22