Module RO4500-KP12

Duration

2 Semester

Turnus of offer

each semester

Credit points

12

Course of studies, specific fields and terms:

• Master Robotics and Autonomous Systems 2019, advanced module, advanced curriculum

Classes and lectures:

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

Workload:

• 30 hours exam preparation
• 150 hours in-classroom work
• 150 hours private studies
• 30 hours in-classroom exercises

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.
• Educational objectives of the seminar Advanced Control and Estimation:
• Students are able to research and understand current literature.
• Students are able to reproduce and evaluate current algorithms based on research literature.
• Students are able reproduce, extend and present results from current research literature.

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:

04.02.2026