In robust control, the discrepancy between a real process and the model chosen for its description, is taken into account for controller design. This is of essential significance in practice, since mathematical models can only describe a real process approximately. Therefore, it is necessary that desired performance requirements such as the suppression of external disturbances and a good reference tracking, as well as the stability of the closed-loop system are not only guaranteed for the nominal model but for a family of models. In this manner, modelling and approximation errors can be addressed. The goal of this project is the development of novel design techniques for (robust) H∞-controllers for the case of dynamical systems with a large state-space dimension and/or with delays. To address this issue, we plan to build optimization-based procedure that constructs reduced controllers by using adaptive interpolatory model reduction techniques on the given plant model.
Conference Papers
- Certifying global optimality for the L∞-norm computation of large-scale descriptor systems, P. Schwerdtner, E. Mengi, and M. Voigt, IFAC-PapersOnLine, 53(2):4279–4284, 2020, 21st IFAC World Congress, Berlin, Germany, https://doi.org/10.1016/j.ifacol.2020.12.2482
- Adaptive sampling for structure-preserving model order reduction of port-Hamiltonian systems, P. Schwerdtner and M. Voigt, IFAC-PapersOnLine, 54(19):143–148, 2021, 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Berlin, Germany, https://doi.org/10.1016/j.ifacol.2021.11.069
- Optimization-based structured reduced order modeling from frequency samples, P. Schwerdtner and M. Voigt, MATHMOD 2022 Discussion Contribution Volume, vol. 17 of ARGESIM Reports, pp. 79–80, ARGESIM Publisher, Vienna, Austria, 2022, https://doi.org/10.11128/arep.17
- Structure-preserving model reduction of port-Hamiltonian systems by optimization, P. Schwerdtner and M. Voigt, 26th International Symposium on Mathematical Theory of Networks and Systems, pp. 444–447, Cambridge, United Kingdom, 2024
Journal Articles
- SOBMOR: Structured optimization-based model order reduction, P. Schwerdtner and M. Voigt, SIAM J. Sci. Comput., 45(2):A502–A529, 2023, https://doi.org/10.1137/20m1380235
- Fixed-order H-infinity controller design for port-Hamiltonian systems, P. Schwerdtner and M. Voigt, Automatica J. IFAC, 152:110918, 2023, https://doi.org/10.1016/j.automatica.2023.110918
- Optimization-based model order reduction of port-Hamiltonian descriptor systems, P. Schwerdtner, T. Moser, V. Mehrmann, and M. Voigt, Systems Control Lett., 182:105655, 2023, https://doi.org/10.1016/j.sysconle.2023.105655
- Structured optimization-based model order reduction for parametric systems, P. Schwerdtner and M. Schaller, SIAM J. Sci. Comput., 47(1):A72-A101, 2025, https://doi.org/10.1137/22M1524928
Preprints
- Port-Hamiltonian system identification from noisy frequency response data, P. Schwerdtner, arXiv preprint arXiv:2106.11355, June 2021, https://doi.org/10.48550/arXiv.2106.11355
Theses
- H∞ Control for Large-Scale Linear Systems, A. Lahr, Masterarbeit, Technische Universität Berlin, Institut für Mathematik, 2021
- Structured Optimization-Based Reduction, Identification, and Control, P. Schwerdtner, Dissertation, Technische Universität Berlin, Institut für Mathematik, 2023, https://depositonce.tu-berlin.de/items/73c79868-a5d2-4571-8b38-2cb0101989e5
Software
