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KTH / Engineering Science / Mathematics / Optimization and Systems Theory

SF2842 Geometric Control Theory


Examiner and lecturer

Xiaoming Hu (hu@math.kth.se), Room 3712, Lindstedtsv. 25, tel. 790 7180.

Teaching assistant

Maja Karasalo (karasalo@math.kth.se), Lindstedtsv. 25, tel. 790 8433.

Course contents

The goal of the course is to give students good knowledge about the fundamental results in the geometric control theory. Here is an introduction to the course.

Course material

Course requirements

There are three homework sets that must be completed. The homework questions will be made available to the students around ten days before the deadline. Successful completion of the homework sets (better than 60% or better than 80%) gives grade E or D. A written exam is required for a grade higher than D. 43 points out of 50 points will guarantee an A. If you fail one set of the homework, you can still get a grade E by obtaining at least 22 points out of 50 points in the final exam.

Homework

  • pdf (Due November 18, 2009)
  • pdf (Due December 1, 2009)
  • pdf (Due December 15, 2009)
Note: The date in parentheses is the last day (before 5 pm) for handing in the written solutions. The homework questions will be made available online about ten days before the deadline.

Some old homework can be downloaded here: Homework 1, Homework 2, and Homework 3.

Written exam

An optional written exam (for grade higher than D) will be held on December 18, 2009, 14:00-19:00. This will be an open-book exam. The exam will consist of five problems that give maximal 50 points. These problems will be similar in type to those in the homeworks and in the exercises. 43 points will guarantee a grade A, 37 a grade B and 31 a grade C. Here is an example of exam and solution.

Schedule for 2009

F=Lecture, Ö=Exercise

Type Day Date Time Hall Topic
F1.Wed 28/10 15-17 D33 Introduction
F2.Thu 29/10 15-17 D33 Invariant subspaces
F3.Fri 30/10 10-12 D42 Invariant subspaces (cont.)
F4.Tue 3/11 15-17 D42 Disturbance decoupling
Ö1.Thu 5/11 13-15 D33 Linear algebra, invariant subspaces
F5.Fri 6/11 13-15 D33 Disturbance decoupling, and Zeros
F6.Tue 10/11 15-17 E33 Zeros and zero dynamics (cont.)
Ö2.Wed 11/11 10-12 E34 Reachability subspaces, V*-algorithm, zero dynamics
F7.Thu 12/11 13-15 D33 Zero dynamics and high gain control
F8.Fri 13/11 13-15 D33 Noninteracting control and tracking
F9. Tue 17/11 15-17 E33 Input-output behavior
F10.Wed 18/11 08-10 E34 Input-output behavior and Output regulation
F11.Thu 19/11 13-15 D33 Output regulation (cont.)
Ö3.Fri 20/11 13-15 D33 Applications of zero dynamics
F12.Tue 24/11 15-17 E33 Nonlinear systems: examples, math preparation
Ö4.Wed 25/11 15-17 D33 Sylvester equation, Output tracking input, Output regulation
F13.Thu 26/11 13-15 D33 Nonlinear systems: controllability, stability
F14.Fri 27/11 13-15 D33 Nonlinear systems: steady state response
Ö5.Tue 1/12 15-17 E33 Nonlinear systems
F15.Wed 2/12 15-17 D33 Center manifold and normal form
F16.Thu 3/12 13-15 D33 Nonlinear systems: zero dynamics and applications
F17.Fri 4/12 10-12 K52 Exact linearization and Consensus problem
F18.Tue 8/12 15-17 E33 Robotic systems
Ö6.Wed 9/12 8-10 D33 Nonlinear control problems







Published by: Optimization and Systems Theory, KTH
Xiaoming Hu

Last updated: 2009-12-06