Dynamical system theory for engineers

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, Measure Theory.

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

Recommended courses

• Analysis IV (MATH 207 or equivalent)

Important concepts to start the course

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

Teaching methods

• Lectures (blackboard, no video), 3h per week
• Exercise session, 1h per week

Expected student activities

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

Assessment methods

1. Mid-term 20%
2. Final exam 80%

Supervision

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

• https://go.epfl.ch/COM-502

Prerequisite for

Classes using methods from linear and nonlinear dynamical systems.