Math @ Duke

Publications [#243784] of Mauro Maggioni
Papers Published
 Bouvrie, J; Maggioni, M, Geometric multiscale reduction for autonomous and controlled nonlinear systems,
in Proc. IEEE Conference on Decision and Control (CDC),
Proceedings of the Ieee Conference on Decision and Control
(December, 2012),
pp. 43204327, IEEE, ISBN 9781467320658 [mostRecentIssue.jsp], [doi]
(last updated on 2019/02/20)
Abstract: Most generic approaches to empirical reduction of dynamical systems, controlled or otherwise, are global in nature. Yet interesting systems often exhibit multiscale structure in time or in space, suggesting that localized reduction techniques which take advantage of this multiscale structure might provide better approximations with lower complexity. We introduce a snapshotbased framework for localized analysis and reduction of nonlinear systems, based on a systematic multiscale decomposition of the statespace induced by the geometry of empirical trajectories. A given system is approximated by a piecewise collection of lowdimensional systems at different scales, each of which is suited to and responsible for a particular region of the statespace. Within this framework, we describe localized, multiscale variants of the proper orthogonal decomposition (POD) and empirical balanced truncation methods for model order reduction of nonlinear systems. The inherent locality of the treatment further motivates control strategies involving collections of simple, local controllers and raises decentralized control possibilities. We illustrate the localized POD approach in the context of a highdimensional fluid mechanics problem involving incompressible flow over a bluff body. © 2012 IEEE.


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