NDLI: Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Willcox, Karen Peherstorfer, Benjamin Kramer, Boris
Copyright Year	2017
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 offline-online strategy for controlling systems with time-varying parameters. During the offline 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 reflects 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 flow through a porous medium. We demonstrate on those models that the proposed method successfully stabilizes the system model in the presence of process noise.
Sponsorship	Defense Advanced Research Projects Agency. U.S. Department of Energy
Starting Page	1563
Ending Page	1586
Page Count	24
File Format	PDF
DOI	10.1137/16M1088958
e-ISSN	15360040
Issue Number	3
Volume Number	16
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2017-08-17
Access Restriction	Subscribed
Subject Keyword	dynamical systems Systems governed by ordinary differential equations low-rank approximations feedback control data-driven reduced models model reduction online adaptive model reduction time-varying parameters
Content Type	Text
Resource Type	Article

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