FEL3340 Introduction to Model Order Reduction

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.