Feedback control for systems with uncertain parameters using online-adaptive reduced models

Boris Kramer, Benjamin Peherstorfer, Karen Willcox

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1563-1586
Number of pages24
JournalSIAM Journal on Applied Dynamical Systems
Volume16
Issue number3
DOIs
Publication statusPublished - Jan 1 2017

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Keywords

  • Data-driven reduced models
  • Dynamical systems
  • Feedback control
  • Low-rank approximations
  • Model reduction
  • Online adaptive model reduction
  • Time-varying parameters

ASJC Scopus subject areas

  • Analysis
  • Modeling and Simulation

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