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Nonlinear model reduction for control of distributed systems: A computer‐assisted study
Author(s) -
Shvartsman Stanislav Y.,
Kevrekidis Ioannis G.
Publication year - 1998
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690440711
Subject(s) - reduction (mathematics) , nonlinear system , controller (irrigation) , stability (learning theory) , computer science , partial differential equation , control theory (sociology) , inertial frame of reference , mathematical optimization , control (management) , mathematics , control engineering , engineering , artificial intelligence , physics , machine learning , quantum mechanics , mathematical analysis , geometry , agronomy , biology
Model reduction methodologies for the partial differential equations modeling distributed parameter systems constitute an important first step in controller design. A systematic computer‐assisted study illustrating the use of two such methodologies (Approximate Inertial Manifolds and the Karhunen‐Loève expansion) in controlling (stabilizing) a nonlinear reaction‐diffusion problem is presented. The approximation quality of the models, issues of computational implementation of the reduction procedure, as well as issues of closed‐loop stability are addressed.