# EL3500 Introduktion till modellreduktion 7,0 hp

## Introduction to Model Order Reduction

In engineering and science it is often desirable to use the simplest mathematical model that "does the job". However, it is often the case that first -principles modeling or system identification result in unnecessarily high- dimensional dynamical systems. Model (order) reduction is about systematic approximation of such dynamical systems.

There are many advantages to work with models with low- dimensional state space. For example, low- dimensional models are often easier to analyze and to simulate. Futhermore, if the model is going to be implemented, for example as a feedback controller, then a low dimension allow us to use cheaper hardware.

#### Utbildningsnivå

Forskarnivå-
#### Kursnivå (A-D)

D #### Huvudområde

#### Betygsskala

P, F

Det finns inget planerat kurstillfälle.

## Lärandemål

After finishing the course, the student will

- be able to distinguish between hard and simple model reduction problems
- be able to apply standard model reduction techniques sush as POD/PCA/SVD to examples that are relevant to the student
- understand the interplay between cotrollability, observability and model reduction
- know the theory behind balanced truncation and Hankel norm approximation
- be able to reduce the order of linear feedback and feedforward controllers while taking the overall system performance into account.

## Kursens huvudsakliga innehåll

There are nine lectures in the course:

Lecture1: Introduction, the model-order-reduction problem. Examples.

Lecture 2: Model truncation, singular perturbation.

Lecture 3: Linear systems: POD/PCA/SVD-based simplifiction.

Lecture 4: Linear systems: Gramians and balanced realizations.

Lecture 5: Balanced truncation and weighted extensions.

Lecture 6: Applications; controller and nonlinear model reduction.

Lecture 7: Optimal model reduction: Hankel norm approximation .

Lecture 8:System identification and model reduction in H2-norm (guestlecture).

Lecture 9: Summary

## Kursupplägg

There are nine lectures and seven exercise sessions in the course. Every set of lecture notes comes with 2-4 hand-in problems. These are to be solved and turned in seven days after they have been handed out. The problems are then solved and discussed in the following exercise session. The student should also do a project preferably relates as much as possible to the student´s own research project.

## Behörighet

This is a graduate level course, but last-year/ advanced undergraduate students may also be admitted.

## Rekommenderade förkunskaper

in order to do well in the course, basic knowledge of state-space methods in systems and controls, linear algebra and some previous experience with Matlab programming is desirable.

## Litteratur

## Examination

## Krav för slutbetyg

To pass, the student needs to complete:

1. at least 75% of the turn-in problems.

2. a smaller project with an approved report.

3. a take-home exam.

## Ges av

EES/Reglerteknik

## Kontaktperson

Henrik Sandberg

## Examinator

Henrik Sandberg <hsan@kth.se>

## Versionsinformation

Kursplan giltig från och med HT2008.

Examinationsinformation giltig från och med HT2008.