Modeling and Reduction of Complex Systems

The module deals with modern methods for structured modeling, energy-based control and order reduction of high-dimensional system models. The topics are important areas of current research, among others at the Chair of Automatic Control. The presented methods allow for a control-oriented approach to complex systems and design problems: The port-Hamiltonian approach is based on structured modeling and puts an emphasis on the power flows. It is very appropriate for the representation of coupled multi-physics systems. Order reduction is necessary to cope efficiently with very high-dimensional models in simulation and computational control. High-order models result for example from the spatial discretization of multi-physics distributed parameter systems.

The choice of their module prepares interested students for research internships and theses in the corresponding research areas of the Chair of Automatic Control. The following topics are presented:

A) Port-Hamiltonian (PH) systems

1. Port-based modeling, Dirac structures and modular PH models
2. PH systems and passivity
3. Integration and calculus with differential forms
4. Conservation and balance laws in PH form
5. PH representation of beam models

B) Model Order Reduction

  1. Introduction
  2. Fundamentals from Linear Algebra
  3. Projection-based Model Order Reduction
  4. Modal Reduction
  5. Balanced Truncation
  6. Krylov Subspace Methods

The lecture given in English in the summer semester, is a Master degree module. After having passed the exam,  you will get 5 ECTS.

The module consists of the weekly
exercise course
and an optional revision exercise.
The revision exercise gives the opportunity
a) to clarify open questions concerning the course's contents and/or to deepen further topics going beyond the scope of the lecture and
b) to prepare for the exam.