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Finite-Horizon Parameterizing Manifolds, and Applications to Suboptimal Control of Nonlinear Parabolic PDEs

Finite-Horizon Parameterizing Manifolds, and Applications to Suboptimal Control of Nonlinear... This article proposes a new approach for the design of low-dimensional suboptimal controllers to optimal control problems of nonlinear partial differential equations (PDEs) of parabolic type. The approach fits into the long tradition of seeking for slaving relationships between the small scales and the large ones (to be controlled) but differ by the introduction of a new type of manifolds to do so, namely the finite-horizon parameterizing manifolds (PMs). Given a finite horizon [0,T] and a low-mode truncation of the PDE, a PM provides an approximate parameterization of the high modes by the controlled low ones so that the unexplained high-mode energy is reduced—in a mean-square sense over [0,T]—when this parameterization is applied. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Finite-Horizon Parameterizing Manifolds, and Applications to Suboptimal Control of Nonlinear Parabolic PDEs

Acta Applicandae Mathematicae , Volume 135 (1) – Sep 26, 2014

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References (124)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer Science+Business Media Dordrecht
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-014-9949-1
Publisher site
See Article on Publisher Site

Abstract

This article proposes a new approach for the design of low-dimensional suboptimal controllers to optimal control problems of nonlinear partial differential equations (PDEs) of parabolic type. The approach fits into the long tradition of seeking for slaving relationships between the small scales and the large ones (to be controlled) but differ by the introduction of a new type of manifolds to do so, namely the finite-horizon parameterizing manifolds (PMs). Given a finite horizon [0,T] and a low-mode truncation of the PDE, a PM provides an approximate parameterization of the high modes by the controlled low ones so that the unexplained high-mode energy is reduced—in a mean-square sense over [0,T]—when this parameterization is applied.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Sep 26, 2014

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