A new framework for H2-optimal model reduction. Issue 3 (4th May 2018)

• Record Type: Journal Article
• Authors: Castagnotto, Alessandro; Lohmann, Boris
• Is Part Of: Mathematical and computer modelling of dynamical systems. Volume 24:Issue 3(2018)
• Page Start: 236
• Page End: 257
• Publication Date: 2018-05-04
• Subjects: Large scale -- model reduction -- model reduction and model simplification -- H2-optimal reduction; Engineering -- Mathematical models -- Periodicals; Computer simulation -- Periodicals; 515.39
• DOI: 10.1080/13873954.2018.1464030
• Languages: English
• ISSNs: 1387-3954

Abstract

ABSTRACT: In this contribution, a new framework forH 2 -optimal reduction is presented, motivated by the local nature of both (tangential) interpolation andH 2 -optimal approximations. The main advantage is given by a decoupling of the cost of reduction from the cost of optimization, resulting in a significant speedup inH 2 -optimal reduction. In addition, a middle-sized surrogate model is produced at no additional cost and can be used e.g. for error estimation. Numerical examples illustrate the new framework, showing its effectiveness in producingH 2 -optimal reduced models at a far lower cost than conventional algorithms. Detailed discussions and optimality proofs are presented for applying this framework to the reduction of multiple-input, multiple-output linear dynamical systems. The paper ends with a brief discussion on how this framework could be extended to other system classes, thus indicating how this truly is a general framework for interpolatoryH 2 reduction.