FEL3340 Introduction to Model Order Reduction 7.0 credits

Linear time-invariant systems, state space, truncation, residualization/singular perturbation, projection, Kalman decomposition, norms, Hilbert spaces L2 and H2, H∞ space, POD, SVD, PCA, Schmidt-Mirsky theorem, optimization in Hilbert spaces, reachability and observability Gramians, matrix Lyapunov equations, balanced realizations, error bounds, frequency-weighted model reduction, balanced stochastic truncation,  controller reduction, small-gain theorem, empirical Gramians, Hankel-norm, Nehari theorem, Adamjan-Arov-Krein lemma, optimal Hankel-norm approximation

After the course, the student should:

·         be able to distinguish between difficult and simple model-reduction problems;

·         have a thorough understanding of Principle Component Analysis (PCA) and Singular Value Decomposition (SVD);

·         understand the interplay between linear operators on Hilbert spaces, controllability, observability, and model reduction;

·         know the theory behind balanced truncation and Hankel-norm approximation;

·         be able to reduce systems while preserving certain system structures, such as interconnection topology;

·         be able to reduce linear feedback controllers while taking the overall system performance into account; and

·         to understand, and be able to contribute to, current research in model order reduction.

Lecture notes, research papers, and part of the books

·         Obinata, G. and Anderson, B.D.O., "Model Reduction for Control System Design", Springer-Verlag, London, 2001.

·         Luenberger, D.G., “Optimization by Vector Space Methods”, Wiley, 1969.

·         Green, M. and Limebeer, D.J.N, “Linear Robust Control”, Dover, 2012.

If the course is discontinued, students may request to be examined during the following two academic years.

• EXA1 - Examination, 7.0 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

·         75 % on homework problems

·         50 % on take-home exam

·         Participation in special focus lectures alt. conducts a project

Henrik Sandberg

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.