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.

## Keywords

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

## 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 20% (conditionally on the Covid situation allowing for it to be taken at EPFL).
2. Final exam 80%

## Supervision

 Office hours Yes Assistants Yes Forum Yes

## 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.

## Prerequisite for

Classes using methods from dynamical systems.

## Dans les plans d'études

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

 Lu Ma Me Je Ve 8-9 ELA2 9-10 10-11 ELA2 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

Mercredi, 8h - 10h: Cours ELA2

Mercredi, 10h - 11h: Exercice, TP ELA2