Modeling and identification (22/23)
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WMMA00705 
Vaknaam  Modeling and identification (22/23) 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester I b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Modeling and Identification (tweejaarlijks 2022/2023)  
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. employ subspace methods for linear dynamical systems to compute models and controllers from measured data 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 inputstateoutput systems. The emphasis is on linear timeinvariant models. These models are very important for applications and admit a detailed and elegant mathematical analysis. Contents: 1. Statespace models, higherorder differential equation models, and transfer matrix descriptions, and how to from one description to another one. In particular, we study the realization problem which is concerned with setting up (minimal) state space models for higherorder differential/difference models and transfer matrices. We also discuss systems with physical structure. 2. Model reduction of linear state space models. In many applications state space models are highdimensional, and need to be approximated by reduced models. We investigate the theory of balancing of linear systems, and show how lowdimensional approximations can be achieved by making use of the controllability and observability Gramian. We also pay attention to structurepreserving model reduction, where we want certain structural characteristics (such as passivity) of the highdimensional model to be preserved. Furthermore, we consider other model reduction methods based on Krylov subspace methods. 3. Identification and datadriven control of linear dynamical systems. In practice, mathematical models of dynamical systems are rarely known a priori, and have to be identified using measured data. We investigate subspace identification methods to obtain state space models from input/output data. We emphasize the notion of persistently exciting data, that turns out to be crucial for successful databased modeling. In addition, we will demonstrate how controllers can be obtained directly from raw data, without the intermediate system identification step. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(During the course, students will receive three sets of takehome assignments. The final grade will be computed as: F = 0.2*H1 + 0.2*H2 + 0.2*H3 + 0.4*WE, where F is the final grade, Hi are the takehome assignments, and WE is the written exam.) 

Vaksoort  master  
Coördinator  dr. ir. B. Besselink  
Docent(en)  dr. ir. B. Besselink ,dr. ir. H.J. van Waarde  
Verplichte literatuur 


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  
Opgenomen in 
