Control-oriented Model Reduction for Parabolic Systems: Approximate Balancing-related Model Reduction Methodsfor Data-sparse Systems

Model reduction is one of the most valuablecontributions of mathematical system theory toapplied mathematics (Jan C. Willems, 2007).In this book, Ulrike Baur investigates modelreduction for parabolic PDEs based on balancedtruncation.Effective implementations of balanced truncation (andof related methods such as singular perturbationapproximation, cross-Gramian model reduction, balanced truncationfor unstable systems)are developed by exploiting the structure of theunderlying PDE problem.This is achieved by a data-sparse approximation ofthe (semi-)discretized differential operator using thehierarchical matrix format and by using the formatted arithmetic in the developedsolvers for different types of matrix equations such as(generalized) Lyapunov, Stein, Sylvester andalgebraic Bernoulli equations.All approaches are well-suited for classes ofpractically relevantproblems and allow the application of balancedtruncation and related methods to systems coming from 2D and 3D FEM and BEM discretizations.