Premium
Optimal experiment design for nonlinear dynamic (bio)chemical systems using sequential semidefinite programming
Author(s) -
Telen Dries,
Logist Filip,
Quirynen Rien,
Houska Boris,
Diehl Moritz,
Impe Jan
Publication year - 2014
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.14389
Subject(s) - semidefinite programming , mathematical optimization , context (archaeology) , fisher information , matrix (chemical analysis) , inverse , sequential quadratic programming , dynamic programming , mathematics , nonlinear system , nonlinear programming , computer science , algorithm , quadratic programming , statistics , chemistry , physics , quantum mechanics , paleontology , geometry , chromatography , biology
Optimal experiment design (OED) for parameter estimation in nonlinear dynamic (bio)chemical processes is studied in this work. To reduce the uncertainty in an experiment, a suitable measure of the Fisher information matrix or variance–covariance matrix has to be optimized. In this work, novel optimization algorithms based on sequential semidefinite programming (SDP) are proposed. The sequential SDP approach has specific advantages over sequential quadratic programming in the context of OED. First of all, it guarantees on a matrix level a decrease of the uncertainty in the parameter estimation procedure by introducing a linear matrix inequality. Second, it allows an easy formulation of E‐optimal designs in a direct optimal control optimization scheme. Finally, a third advantage of SDP is that problems involving the inverse of a matrix can be easily reformulated. The proposed techniques are illustrated in the design of experiments for a fed‐batch bioreactor and a microbial kinetics case study. © 2014 American Institute of Chemical Engineers AIChE J , 60: 1728–1739, 2014