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Generation of discrete first‐ and second‐order sensitivities for single shooting
Author(s) -
Barz Tilman,
Kraus Robert,
Zhu Liming,
Wozny Günter,
ArellanoGarcia Harvey
Publication year - 2012
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.13720
Subject(s) - hessian matrix , legendre polynomials , mathematics , collocation (remote sensing) , jacobian matrix and determinant , algebraic number , differential (mechanical device) , computer science , mathematical optimization , mathematical analysis , engineering , machine learning , aerospace engineering
Abstract In this work, an approach to the forward generation of discrete first‐ and second‐order sensitivities is proposed. For this purpose, an algorithm has been developed, which can basically be applied to general implicit differential‐algebraic equation (DAE) systems. Moreover, the approach has been tailored to both the generation of directional derivatives and sensitivities with respect to discontinuous control trajectories. The implementation of the method is discussed here for the orthogonal collocation method based on Legendre–Gauss–Radau points and considering the linear implicit DAE type, which arises in problems related to chemical engineering. Lastly, the approach has been applied to three case studies of different complexities. The corresponding performance for the generation of Jacobian and Hessian information is discussed in detail. © 2012 American Institute of Chemical Engineers AIChE J, 58: 3110–3122, 2012