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Process Systems Engineering
Generation of discrete first- and second-order sensitivities for single shooting
Article first published online: 24 JAN 2012
DOI: 10.1002/aic.13720
Copyright © 2012 American Institute of Chemical Engineers (AIChE)
Additional Information
How to Cite
Barz, T., Kraus, R., Zhu, L., Wozny, G. and Arellano-Garcia, H. (2012), Generation of discrete first- and second-order sensitivities for single shooting. AIChE J., 58: 3110–3122. doi: 10.1002/aic.13720
Publication History
- Issue published online: 10 SEP 2012
- Article first published online: 24 JAN 2012
- Accepted manuscript online: 22 DEC 2011 02:04PM EST
- Manuscript Revised: 20 DEC 2011
- Manuscript Received: 19 JUL 2011
- Abstract
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- Cited By
Keywords:
- dynamic optimization;
- quasi-sequential approach;
- orthogonal collocation;
- forward generation of first- and second- order sensitivities
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