Introduction to Model Order Reduction
Ph.D. course, 7 credits, Spring 2014
In engineering and science it is often desirable to use the simplest possible mathematical model that “does the job”. Firstprinciples modeling or system identification commonly result in unnecessarily highdimensional mathematical models. Model (order) reduction concerns systematic approximation of such models. There are many advantages of working with models with a lowdimensional state space. For example, lowdimensional models are easier to analyze and much faster to simulate. Model reduction methods have successfully been used to solve largescale problems in areas such as control engineering, signal processing, image compression, fluid mechanics, and power systems. In this Ph.D. course, we give an introduction to some powerful available reduction techniques, as well as to the required underlying mathematics.
Instructors:
Henrik Sandberg (responsible), Bart Besselink, and Madhu N. Belur (IIT Bombay)
Meeting times: First lecture scheduled for March
31^{st}, 13:1515:00 (see schedule below).
Location: To be announced. Enroll to receive course updates.
Grading: Grade (pass/fail) is based on
turnin exercises (50%) and written exam (50%).
Prerequisites:
Basic linear systems theory (statespace
realizations, Laplace transforms etc.), matrix theory, and basic
MATLABprogramming.
To enroll, please send an email to Henrik Sandberg
(Here some lectures notes
from the course in 2010 can be found.)
Program
(dates and times subject to change)
Date 
Time 
Event 
Room 
Lecturer 
Topic 
20140331 
13:1515:00 
Lecture 1 
Q13 
HS 
Introduction. The
model reduction problem. [Slides, Course
Program] 
20140402 
13:1515:00 
Lecture 2 
L41 
HS 
Model truncation,
singular perturbation. [Notes] 
20140404 
10:1512:00 
Exercise 1 
Q24 
HS 
Review of linear
systems and Hilbert spaces etc. 
20140407 
13:1515:00 
Lecture 3 
Q24 
BB 
POD/PCA/SVDbased
reduction. [Notes] 
20140409 
13:1515:00 
Lecture 4 
Q24 
BB 
Gramians
and balanced realizations. [Notes] 
20140424 
13:1515:00 
Exercise 2 
Q24 
HS/BB 
Exercises due April
17 
20140425 
13:1515:00 
Lecture 5 
Q24 
BB 
Balanced truncation [Notes, building.mat] 
20140428 
10:1512:00 
Lecture 6 
Q24 
BB 
Weighted balanced
truncation and controller reduction. Nonlinear model reduction [Notes, exercise_55.zip] 
20140505 
10:1512:00 
Lecture 7 
Q13 
HS 
Optimal model order
reduction in the Hankel norm. [Notes] 
20140507 
15:1517:00 
Lecture 8 
Q24 
HS 
Optimal model order
reduction in the H2/Hinfinity norms. 
20140509 
10:1512:00 
Lecture 9 
Q13 
MB 
Behavioral approach,
kernel representations 
20140512 
13:1515:00 
Lecture 10 
Q13 
MB 
Controllability,
passivity, dissipativity, storage functions 
20140514 
13:1515:00 
Lecture 11 
Q24 
MB 
Maximum and minimum
storage functions 
20140516 
10:1512:00 
Exercise 3 
Q13 
HS/BB 
Exercises due May 14 
20140519 
13:1515:00 
Lecture 12 
Q13 
MB 
The LQ problem, Hinfinitynorm as dissipativity 
20140521 
13:1515:00 
Lecture 13 
L41 
MB 
Passivity preserving
model reduction 
20140526 
10:1512:00 
Lecture 14 
Q13 
MB 
Dissipativity preserving model reduction 
20140528 
13:1515:00 
Exercise 4 
Q24 
MB 

·
Antoulas,
A.C., "Approximation of LargeScale Dynamical Systems", Society for
Industrial and Applied Mathematics, 2005.
· Obinata, G. and Anderson, B.D.O., "Model Reduction for Control System Design", SpringerVerlag, London, 2001.
·
Doyle,
J.C., Francis, B., and Tannenbaum, A., "Feedback
Control Theory", Macmillan Publishing Co., 1990.
· Green, M., and Limebeer, D.J.N., "Linear Robust Control", Prentice Hall, Englewood Cliffs, 1995.
· Zhou K., Doyle, J.C., and Glover, K., "Robust and Optimal Control", Prentice Hall, Upper Saddle River, 1996.