Stabilization of linear time‐varying reduced‐order models: A feedback controller approach
Abstract
Many of the commonly used methods in model‐order reduction do not guarantee stability of the reduced‐order model. This article extends the eigenvalue reassignment method of stabilization of linear time‐invariant ROMs, to the more general case of linear time‐varying systems. Through a postprocessing step, the ROM is controlled to ensure the stability while enhancing/maintaining its accuracy using a constrained nonlinear lease‐square minimization problem. The controller and the input signals are defined at the algebraic level, using left and right singular vectors of the reduced system matrices. The choice provides a control on the upper bound of the growth of the energy of the reduced system. The optimization problem is applied to several time‐invariant, time‐periodic, and time‐varying problems, and the reproductive and predictive capabilities of the proposed method, with respect to novel inputs and the system parameters, are evaluated.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 23, 2020
- Source ID
- 10.1002/nme.6489
Entities
People
- Maciej Balajewicz
- Rambod Mojgani
Organizations
- Air Force Office of Scientific Research
- University of Illinois Urbana–Champaign