Optimal control of multiscale systems using reduced-order models

Carsten Hartmann; Juan C. Latorre; Wei Zhang; Grigorios A. Pavliotis

doi:10.3934/jcd.2014.1.279

Article Contents

2014, Volume 1, Issue 2: 279-306. Doi: 10.3934/jcd.2014.1.279

This issue Previous Article Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools Next Article Lattice structures for attractors I

Optimal control of multiscale systems using reduced-order models

1.
Institute of Mathematics, Freie Universität Berlin, 14195 Berlin
2.
Department of Mathematics, Imperial College London, London SW7 2AZ

Received: May 31, 2014

Revised: August 31, 2014

Published: May 2014

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Abstract

We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal control computed from the reduced-order model to control the original, high-dimensional system? The strategy ``first reduce, then optimize''---rather than ``first optimize, then reduce''---is motivated by the fact that solving optimal control problems for high-dimensional multiscale systems is numerically challenging and often computationally prohibitive. We state sufficient and necessary conditions, under which the ``first reduce, then control'' strategy can be employed and discuss when it should be avoided. We further give numerical examples that illustrate the ``first reduce, then optmize'' approach and discuss possible pitfalls.

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Mathematics Subject Classification: Primary: 93E20, 93C70; Secondary: 49L20.

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