Low-Dimensional Approximation for Control of Spatio-Temporal Processes Using Principal Interaction Patterns

Xiang Ping Cao; Zhao Yang Li; Mei Xing Liu

doi:10.4028/www.scientific.net/AMR.591-593.1217

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 591-593Low-Dimensional Approximation for Control of...

Low-Dimensional Approximation for Control of Spatio-Temporal Processes Using Principal Interaction Patterns

Abstract:

Although the first-principal models of the spatio-temporal processes can accurately predict nonlinear and distributed dynamical behaviors, their infinite-dimensional nature does not allow their directly use. In this note, low-dimensional approximations for control of spatio-temporal processes using principal interaction patterns are constructed. Advanced model reduction approach based on spatial basis function expansion together with Galerkin method is used to obtain the low-dimensional approximation. Spatial structure called principal interaction patterns are extracted from the system according to a variational principle and used as basis functions in a Galerkin approximation. The simulations of the burgers equations has illustrated that low-dimensional approximation based on principal interaction patterns for spatio-temporal processes has smaller errors than more conventional approaches using Fourier modes or Empirical Eigenfunctions as basis functions.

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Periodical:

Advanced Materials Research (Volumes 591-593)

Pages:

1217-1220

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.591-593.1217

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Online since:

November 2012

Authors:

Xiang Ping Cao, Zhao Yang Li, Mei Xing Liu

Keywords:

Basis Function, Galerkin Method, Low-Dimensional Approximation, Principal Interaction Pattern, Spatio-Temporal Process

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