Module RO4500-KP08

Duration

2 Semester

Turnus of offer

each semester

Credit points

8

Course of studies, specific fields and terms:

• Master Robotics and Autonomous Systems 2019, optional subject, Elective

Classes and lectures:

• Graphical Models in Systems and Control (exercise, 1 SWS)
• Graphical Models in Systems and Control (lecture, 2 SWS)
• Linear Systems Theory (exercise, 2 SWS)
• Linear Systems Theory (lecture, 2 SWS)

Workload:

• 30 hours in-classroom exercises
• 70 hours private studies
• 120 hours in-classroom work
• 20 hours exam preparation

Contents of teaching:

• Contents of Linear Systems Theory:
• Introduction: Vectors and matrices
• Introduction: Linear programming
• Vector spaces in finite dimensions, sequence spaces, function spaces
• Subspaces, orthogonal complement
• Norm, convergence, Cauchy sequence, completeness
• Inner product, Cauchy Schwarz inequality, adjoint
• Projection Theorem, Gram Schmidt procedure
• Linear operator, eigenvalues, eigenvectors, Jordan normal form
• Spectral Mapping Theorem
• Singular value decomposition and operator norms
• Linear state space models in continuous and discrete time
• Laplace transform and z-transform
• Fundamental solution to linear systems state equations
• Controllability and observability, Cayley Hamilton Theorem
• Stability of state space models
• State feedback and observer design
• Optimal control and estimation (LQR, Kalman Filter)
• Content of Graphical Models in Systems and Control:
• Introduction to Probability Theory, Discretely and Continuously Distributed Random Variables
• Fundamentals on Probabilistic Graphical Models
• Forney-Style Factor Graphs as a Probabilistic Graphical Model
• Message Passing via Sum- and Max-Produkt Algorithms
• Gaussian Message Passing
• State Estimation (Kalman Filtering and Smoothing including Nonlinear Extensions)
• Parameter Estimation via Expectation Maximization
• Expectation Propagation
• Control on Factor Graphs
• Content of the seminar:
• Current state-of-the-art algorithms in stochastic signal processing, estimation, system identification and control.

Qualification-goals/Competencies:

• Educational objectives for course Linear Systems Theory:
• Students are familiar with the important basic concepts of linear algebra.
• Students have a solid background in the theory of linear systems in continuous and disrete time.
• Students are able to model linear systems in mechanical and electrical domain from first principles.
• Students are able to solve the state equations and analyze systems in the time and frequency domain.
• Students improve their problem solving and mathematical skills.
• Students develop their techniques for logical reasoning and and rigorous proofs.
• Students are enabled to perform reseaerch in the field of systems and control theory.
• Educational objectives for course Graphical Models in Systems and Control:
• Students develop and extend their fundamental knowledge on probability theory and the transformation of discretely as well as continuously distributed random variables.
• Students can understand simple linear algorithms, such as the Kalman filter, with the help of graphical probabilistic models.
• Students can combine elements of probabilistic algorithms to novel ones with the help of graphical probabilistic models.
• Students can understand, extend and apply advanced algorithms in signal processing, parameter and state estimation as well as control to relevant problems with the help of graphical probabilistic models.

Grading through:

• Written or oral exam as announced by the examiner

Responsible for this module:

• Prof. Dr. Philipp Rostalski
• Prof. Dr. Georg Schildbach

Teacher:

• Institute for Electrical Engineering in Medicine
• Prof. Dr. Georg Schildbach
• Prof. Dr.-Ing. Christian Herzog

Literature:

• Loeliger, Hans-Andrea; Dauwels, Justin; Hu, Junli; Korl, Sascha; Ping, Li; Kschischang, Frank R. : The Factor Graph Approach to Model-Based Signal Processing Proc. IEEE, Vol. 95, No. 6, 2007 /li>
• Loeliger, Hans-Andrea : An Introduction to factor graphs IEEE Signal Process. Mag., Vol. 21, No. 1, 2004 /li>
• Hoffmann, Christian; Rostalski, Philipp : Current Publications from Research at the IME
• Miscellaneous : Current Publications from Research

Language:

• offered only in English

Notes:

Last Updated:

05.02.2026