Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models
Name
16m1088958.pdf
Size
2.07 MB
Format
Adobe PDF
Checksum (MD5)
aa8256eed4578410086b92853454c4ce
Author(s)
Kramer, Boris
Peherstorfer, Benjamin
Willcox, Karen E
Date Issued
August 2017
Journal
SIAM Journal on Applied Dynamical Systems
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Kramer, Boris, Benjamin Peherstorfer, and Karen Willcox. “Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models.” SIAM Journal on Applied Dynamical Systems 16, no. 3 (January 2017): 1563–1586.
Version
Final published version
Abstract
We consider control and stabilization for large-scale dynamical systems with uncertain, time-varying parameters. The time-critical task of controlling a dynamical system poses major challenges: using large-scale models is prohibitive, and accurately inferring parameters can be expensive, too. We address both problems by proposing an offine-online strategy for controlling systems with time- varying parameters. During the offine phase, we use a high-fidelity model to compute a library of optimal feedback controller gains over a sampled set of parameter values. Then, during the online phase, in which the uncertain parameter changes over time, we learn a reduced-order model from system data. The learned reduced-order model is employed within an optimization routine to update the feedback control throughout the online phase. Since the system data naturally reects the uncertain parameter, the data-driven updating of the controller gains is achieved without an explicit parameter estimation step. We consider two numerical test problems in the form of partial differential equations: a convection-diffusion system, and a model for ow through a porous medium. We demonstrate on those models that the proposed method successfully stabilizes the system model in the presence of process noise.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/16M1088958
