Course Syllabus for

# Nonlinear Control Theory Ickelinjär reglerteori

## FRT026F, 7.5 credits

Valid from: Autumn 2021
Decided by: Professor Thomas Johansson
Date of establishment: 2021-09-07

## General Information

Division: Automatic Control
Course type: Third-cycle course
Teaching language: English

## Aim

The goal of the course is to provide good knowledge and practice the ability to use classical as well as modern analysis and design methods for nonlinear control systems.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• know and understand simple and advanced methods for nonlinear control
• know the strengths and limitations of state-of-the art nonlinear control theory

Competences and Skills

For a passing grade the doctoral student must

• know how to identify and define nonlinear control problems
• be able to use numerical software (e.g. Matlab) to solve advanced nonlinear control problems

Judgement and Approach

For a passing grade the doctoral student must

• understand how to match different theoretical tools to different practical problems
• show ability for teamwork and group collaboration

## Course Contents

Lyapunov theory for autonomous and time-varying systems - Small-gain theory - Absolute stability - Integral quadratic constraints - Passivity - Center manifold theorem - Stability of periodic and perturbed systems - Averaging, Singular perturbations, Geometric control theory - Feedback linearization - Nonlinear design tools (backstepping, high gain control)

## Course Literature

Khalil, H. K.: Nonlinear Systems 3rd ed. Prentice Hall, 2002. ISBN 0130673897.
There are significant changes between the 2nd and 3rd addition, so be sure to obtain the 3rd edition if pursuing this course.

## Instruction Details

Types of instruction: Lectures, exercises

## Examination Details

Examination format: Written exam
Examiner:

Admission requirements: PhD student engineering/maths - basic course in automatic control FRTF05
Assumed prior knowledge: Familiarity with the contents from the masters level course: nonlinear control and servo systems FRTN05

## Further Information

Previous incarnations of the course including all lecture material can be found here: https://www.control.lth.se/education/doctorate-program/nonlinear-control-theory/nonlinear-control-theory-2017/

## Contact and Other Information

Course coordinators:

Web page: https://canvas.education.lu.se/courses/14608