The course covers control theory for nonlinear dynamic systems, including:

- analysis of input and output stability, for example with the low-gain theorem and the circle criterion

- stability analysis of equilibrium points through linearization and Lyapunov methods

- analysis of stability of passive systems

- design and analysis of closed-loop control for nonlinear systems through linearization, feedback linearization and Lyapunov-based methods

- design and analysis of sliding mode control

- observers for nonlinear systems

- setpoint control and setpoint tracking

- simulation of nonlinear dynamic models, including examples from several scientific applications.

After passing the course, the student should be able to:

1. model and analyze nonlinear dynamic systems that arise in engineering and applied scientific fields, such as mechanics, robotics, biological or epidemiological systems, and network systems, using appropriate mathematical representations and stability concepts

2. apply methods for nonlinear control systems and observer design – including Lyapunov-based methods, feedback linearization, passivity, and high-gain control and sliding mode control – to analyze stability and achieve desired control or management

3. use simulation tools to evaluate the behavior of nonlinear systems and control solutions, and critically reflect on model assumptions and limitations and communicate conclusions.

The course is mainly based on the textbook Khalil, H. K., Nonlinear Control, (Global edition, 2015, Pearson Education Ltd, ISBN 978-1-292-06050-7). 

Lecture notes, exercises, and homeworks are found in digital form in Canvas.

You will need a Python environment on your computer for this course.

Students at KTH with a permanent disability can get support during studies from Funka:

Funka - compensatory support for students with disabilities

Please inform the course coordinator if you have special needs not related to the written exam, and show your certificate from Funka.

• Support measures under code R (i.e. adjustments related to space, time, and physical circumstances, e.g. longer writing time) are always granted.
• Support measures under code P (pedagogical measures) may be granted or rejected by the examiner after you have applied for this in accordance with KTH rules. Support measures under code P are usually always granted for courses given at EECS.

• INLA - Homework, 2.5 credits, grading scale: P, F
• INLB - Home work, 2.5 credits, grading scale: P, F
• TENT - Written exam, 2.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

If the course is discontinued, students may request to be examined during the following two academic years.

The course is divided into four modules. Each module is examined by a homework assignment (Homework 1-4), and one exam problem. 

Homework (INLA)

INLA consists of Homework 1 and 2. These are problems that should be solved in Python in groups of 2, and submitted on the due date.

To get a pass grade (P) on INLA, you need 6/10 points on each of Homework 1 and 2. For each of the homeworks assignments, if you get  9/10 points, you will get one bonus point on the corresponding exam problem. The bonus points are only counted for the first original exam, not for any later re-exams.

Homework (INLB )

INLB consists of Homework 3 and 4. These are problems that should be solved in Python in groups of 2, and submitted on the due date.

To get a pass grade (P) on INLB, you need 6/10 points on each of Homework 1 and 2. For each of the homework assignments, if you get  9/10 points, you will get one bonus point on the corresponding exam problem. The bonus points are only counted for the first original exam, not for any later re-exams.

Written exam (TENT)

The exam will have 5 problems: one per module and one additional, more advanced problem. The written exam is solved individually.

Including the bonus points, the final exam will decide the final grade (which also requires pass grade on INLA and INLB). There are five problems with max 10 points per problem.

Grade Fx: 21 points or more.

Grade E: 23 points or more.

Grade D: 28 points or more.

Grade C: 33 points or more.

Grade B: 38 points or more.

Grade A: 43 points or more.

Formulate and apply theory within nonlinear control

E: to solve basic problems

D: to solve advanced problems within some part of the course

C: to solve advanced problems within several parts of the course

B: to solve advanced problems with all parts of the course or to solve problems combining several parts of the course

A: to solve advanced problems within all parts of the course and to solve problems combining several parts of the course.

Students with Fx on the written exam should contact the examiner for an opportunity for supplementary examination to grade to E. 

Students with F on some homework assignements will be given the chance to resubmit again after the written exam if, and only if, the written exam is passed. The same chance is given after the re-exam.

Homework assignments are submitted and corrected in Canvas.

The result on the writen exam is reported directly via LADOK.

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Code of honor

In this course, the EECS code of honor applies, see: http://www.kth.se/en/eecs/utbildning/hederskodex.