02.10.2024 - 4 pm (CEST) - Philipp Schulze (TU Berlin)

Title: 

Structure-Preserving Model Reduction for Dissipative and Port-Hamiltonian Systems

Abstract: 

Model order reduction (MOR) is a powerful tool for reducing the computational effort in applications where a computational model needs to be evaluated multiple times, e.g., in control and optimization. MOR aims to replace the full-order model (FOM) by a reduced-order model (ROM) which should be cheap to evaluate and sufficiently accurate. In many applications it is also desirable to preserve important properties of the FOM such as stability or passivity. One possibility to guarantee this preservation is to use MOR schemes which preserve a dissipative or port-Hamiltonian structure. While there are structure-preserving variants of the most common MOR techniques available, these methods typically lack computable a priori error bounds and suffer from a loss of accuracy in comparison to their non-structure-preserving counterparts. Moreover, these techniques are based on linear subspace approximations of the FOM state and such linear approaches usually perform poorly for transport-dominated systems.

In the first part of this talk, we present a structure-preserving balancing-based MOR approach which allows to provide computable a priori error bounds. Furthermore, we demonstrate that the accuracy of the ROM may be significantly improved by replacing the FOM Hamiltonian by another one which is based on an extremal solution of the corresponding Kalman-Yakubovich-Popov inequality. In the second part of this talk, we address the question of how to construct structure-preserving MOR schemes when using a nonlinear approximation ansatz, which is especially relevant in the context of transport-dominated systems. For a special class of nonlinear ansatzes, we demonstrate that structure-preserving ROMs may be obtained based on a weighted residual minimization scheme. The effectiveness of the presented approaches is demonstrated by means of numerical examples.

The first part of this talk is based on joint work with Tobias Breiten and Riccardo Morandin.

06.11.2024 - 4 pm (CET) - Dorothée Normand-Cyrot (Laboratoire des Signaux et Systèmes, Paris)

Title: About a class of discrete-time and sampled-data Hamiltonian structures

Abstract: Port-Hamiltonian structures have a pervasive impact in numerous applied domains enlarging the more traditional mechanical one. While these structures are unequivocally characterized in the continuous-time domain, several descriptions are proposed in the literature when referring to discrete-time or sampled dynamics. In this talk we discuss a description of port-Hamiltonian structures in discrete time that makes reference to the notion of average passivity, introduced to deal with systems without throughput. Exploiting the average passivity property of these forms, we show how damping feedback and energy-based control strategies can be designed. Then, we investigate the sampled-data case and show how these forms set in discrete-time can be recovered under time-integration through modification of the interconnection and dissipation matrices characterizing the continuous-time dynamics. Some simulations are presented to illustrate analysis and control performances.
 

04.12.2024 - 4 pm (CET) - Timo Reis (TU Ilmenau) 

08.01.2025 - 4 pm (CET) - Claudia Totzeck (BU Wuppertal)