PhD Courses in Denmark

Welcome to Nonlinear Control Theory

Description: 

Virtually all physical systems are nonlinear in nature. Sometimes, however, it is possible to describe the operation of a physical system by a linear model e.g., as a set of ordinary linear differential equations. This is the case, for example, if the mode of operation of the physical system does not deviate too much form the nominal set of operating conditions i.e., one can linearize the system.  Thus the analysis of linear systems occupies an important place in system theory.  But in analyzing the behavior of a physical system, one often encounters situations where the linear (or linearized) model is inadequate or inaccurate e.g., when the states or inputs of the system is constrained; that is the time when concepts of this course may prove very useful.

The course comprises an introduction to nonlinear control systems. It discusses the notions of stability such as stability in Lyapunov sense, asymptotic, and exponential stability. It puts forward tests for checking if a system is stable based on behaviour of a so-called Lyapunov function. Nonlinear control methods such as passivity-based control and sliding mode control will be introduced. We extend the notion of Lyapunov stability to systems with input i.e., input-to-state stability, and show how Lyapunov stability is related to input-output stability.   If time permits we will look at frequency domain analysis of feedback system represented by a feedback connection between a linear dynamical system and a nonlinear dynamical system e.g., a linear time-invariant system with saturation.

Prerequisites: 

A basic knowledge of mathematics as obtained through undergraduate engineering studies.

Organizer: 

John Leth

Lecturers: 

John Leth and Jan Dimon Bendtsen

ECTS: 2

Time: 26, 27, 28 May & 2, 3, 4 June

Place: Aalborg University

Zip code: 9220

City: Aalborg

Maximal number of participants: 30

Deadline: 5 May

Important information concerning PhD courses: 

There is a no-show fee of DKK 3,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before the start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately four months before start of the course.

We cannot ensure any seats before the deadline for enrolment, all participants will be informed after the deadline, approximately 3 weeks before the start of the course.

To attend courses at the Doctoral School in Medicine, Biomedical Science and Technology you must be enrolled as a PhD student.

For inquiries regarding registration, cancellation or waiting list, please contact the PhD administration at aauphd@adm.aau.dk When contacting us please state the course title and course period. Thank you.