TY - JOUR

T1 - A general analysis of approximate lumping in chemical kinetics

AU - Li, Genyuan

AU - Rabitz, Herschel

N1 - Funding Information:
Acknowledgements-The authors acknowledge support from the Office of Naval Research and the Air Force Office of Scientific Research.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1990

Y1 - 1990

N2 - A general analysis of approximate lumping is presented. This analysis can be applied to any reaction system with n species described by dy/dt =f(y), where y is an n-dimensional vector in a desired region Ω, and f(y) is an arbitrary n-dimensional function vector. Here we consider lumping by means of a rectangular constant matrix M (i.e. ŷ = My, where M is a row-full rank matrix and ŷ has dimension n̂ not larger than n). The observer theory initiated by Luenberger is formally employed to obtain the kinetic equations and discuss the properties of the approximately lumped system. The approximately lumped kinetic equations have the same form dŷ/dt = Mf/My) as that for exactly lumped ones, but depend on the choice of the generalized inverse M of M. {1,2,3,4}-inverse is a good choice of the generalized inverse of M. The equations to determine the approximate lumping matrices M are presented. These equations can be solved by iteration. An approach for choosing suitable initial iteration values of the equations is illustrated by examples.

AB - A general analysis of approximate lumping is presented. This analysis can be applied to any reaction system with n species described by dy/dt =f(y), where y is an n-dimensional vector in a desired region Ω, and f(y) is an arbitrary n-dimensional function vector. Here we consider lumping by means of a rectangular constant matrix M (i.e. ŷ = My, where M is a row-full rank matrix and ŷ has dimension n̂ not larger than n). The observer theory initiated by Luenberger is formally employed to obtain the kinetic equations and discuss the properties of the approximately lumped system. The approximately lumped kinetic equations have the same form dŷ/dt = Mf/My) as that for exactly lumped ones, but depend on the choice of the generalized inverse M of M. {1,2,3,4}-inverse is a good choice of the generalized inverse of M. The equations to determine the approximate lumping matrices M are presented. These equations can be solved by iteration. An approach for choosing suitable initial iteration values of the equations is illustrated by examples.

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U2 - 10.1016/0009-2509(90)85020-E

DO - 10.1016/0009-2509(90)85020-E

M3 - Article

AN - SCOPUS:0025628847

SN - 0009-2509

VL - 45

SP - 977

EP - 1002

JO - Chemical Engineering Science

JF - Chemical Engineering Science

IS - 4

ER -