Modeling and identification (19/20)

Faculteit Science and Engineering
Jaar 2020/21
Vakcode WMMA007-05
Vaknaam Modeling and identification (19/20)
Niveau(s) master
Voertaal Engels
Periode semester I a
ECTS 5
Rooster rooster.rug.nl

Uitgebreide vaknaam Modeling and Identification (tweejaarlijks 2019/2020)
Leerdoelen At the end of the course, the student is able to:
1. recognise different representations of linear dynamical systems and is able to transfer between them
2. apply methods for model reduction of linear dynamical systems and reproduce the proofs of their properties
3. apply methods for identification of linear dynamical systems
4. apply the material presented in the course to formulate and prove extensions of results from the course
Omschrijving This course is concerned with the mathematical analysis and identification of dynamical input-state-output systems. The emphasis is on linear time-invariant models. These models are very important for applications and admit a detailed and elegant mathematical analysis.

Contents:
1. State space models, higher-order differential equation models, and transfer matrix descriptions, and how to switch from one description into another one. In particular, we study the realization problem which is concerned with setting up (minimal) state space models for higher-order differential/difference models and transfer matrices. Systems with physical structure.
2. Model reduction of linear state space models. In many applications state space models are high-dimensional, and need to be approximated by reduced models. In particular we investigate the theory of balancing of linear systems, and show how low-dimensional approximations can be achieved by making use of the controllability and observability Gramian. We also pay attention to structure-preserving model reduction, where we want certain structural characteristics (such as passivity) of the high-dimensional model to be preserved. Furthermore, we consider other model reduction methods based on Krylov subspace methods.
3. Identification of linear dynamical systems by subspace identification.
Uren per week
Onderwijsvorm Hoorcollege (LC)
Toetsvorm Opdracht (AST), Schriftelijk tentamen (WE)
(During the course, students will receive three sets of homework problems. The final grade will be computed as : FG = 0.2 H1 + 0.2 H2 + 0.2 H3 + 0.4 Ex, where FG is the final grade, Hi is the ith homework, and Ex the grade for the written exam. See for more infromation the remarks.)
Vaksoort master
Coördinator dr. ir. B. Besselink
Docent(en) dr. ir. B. Besselink
Verplichte literatuur
Titel Auteur ISBN Prijs
Background material (optional reading):
A Course in Robust Control Theory, Springer, 1991
G.E. Dullerud, F. Paganini
Background material (optional reading):
A Linear System Primer, Birkhauser, 2007.
P.J. Antsaklis, A.N. Michel
Background material (optional reading):
Mathematical control theory, TAM 6, Springer, 1998.
E. D. Sontag
Entreevoorwaarden The course assumes prior knowledge in system theory, such as from the course units Project Systems Theory and Advanced Systems Theory within the BSc programme (Applied) Mathematics.
Opmerkingen The first assignment will focus on the topic of realization theory.
The second assignment will focus on the topic of model reduction.
The third assignment will focus on further aspects of model reduction as well as on the topic of system identification.
The final written exam is an open book exam

This course was registered last year with course code WIMI-10
Opgenomen in
Opleiding Jaar Periode Type
MSc Applied Mathematics: Systems and Control  (MSc Applied Mathematics: Systems and Control) - semester I a keuzegroep
MSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester I a
Tweejaarlijkse vakken  (Oneven jaren) - semester I a -