Real-Time Ensemble Control with Reduced-Order Modeling
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Lin-2014-REAL-TIME ENSEMBLE C.pdf
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Author(s)
Lin, Binghuai
McLaughlin, Dennis
Date Issued
August 2014
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Lin, Binghuai, and Dennis McLaughlin. “Real-Time Ensemble Control with Reduced-Order Modeling.” SIAM Journal on Scientific Computing 36, no. 4 (January 2014): B749–B775. © 2014 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
The control of spatially distributed systems is often complicated by significant uncertainty about system inputs, both time-varying exogenous inputs and time-invariant parameters. Spatial variations of uncertain parameters can be particularly problematic in geoscience applications, making it difficult to forecast the impact of proposed controls. One of the most effective ways to deal with uncertainties in control problems is to incorporate periodic measurements of the system's states into the control process. Stochastic control provides a convenient way to do this, by integrating uncertainty, monitoring, forecasting, and control in a consistent analytical framework. This paper describes an ensemble-based approach to closed-loop stochastic control that relies on a computationally efficient reduced-order model. The use of ensembles of uncertain parameters and states makes it possible to consider a range of probabilistic performance objectives and to derive real-time controls that explicitly account for uncertainty. The process divides naturally into forecast/update and forecast/control steps carried out recursively and initialized with a prior ensemble that describes parameter uncertainty. The performance of the ensemble controller is investigated here with a numerical experiment based on a solute transport control problem. This experiment evaluates the performance of open- and closed-loop controllers with full and reduced-order models as well as the performance obtained with a controller based on perfect knowledge of the system and the nominal performance obtained with no control. The experimental results show that a closed-loop controller that relies on measurements consistently performs better than an open-loop controller that does not. They also show that a reduced-order forecasting model based on offline simulations gives nearly the same performance as a significantly more computationally demanding full-order model. Taken together, these results confirm that reduced-order ensemble closed-loop control is a flexible and efficient option for uncertain spatially distributed systems.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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DOI of Published Version
https://doi.org/10.1137/130921878
