Modeling and identification (21/22)

Uitgebreide vaknaam	Modeling and Identification (tweejaarlijks 2021/2022)
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 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. We also discuss 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. 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 and data-driven 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 data-based 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 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 Course material will be provided during the lectures.
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
Opgenomen in	Opleiding Jaar Periode Type MSc Applied Mathematics: Systems and Control  (MSc Applied Mathematics: Systems and Control) - semester II b keuzegroep MSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester II b Tweejaarlijkse vakken  (Oneven jaren) - semester II b -