The DOI matches its Crossref record; 12 of the 12 references it cites were found in a registry or an index.
On the optimization of differential‐algebraic process systems
Abstract
Many chemical engineering problems require the optimization of systems of differential and algebraic equations. Here a method is presented based on finite‐element collocation, which converts differential equations to algebraic residual equations with unknown coefficients. A nonlinear program is then formulated, with residuals incorporated as equality constraints and coefficients as decision variables. Also, adaptive knot placement is used to minimize the approximation error, with necessary and sufficient conditions for optimal knot placement incorporated as additional equality constraints in the nonlinear program. All equality constraints are then solved simultaneously with the optimization problem, thus requiring only a single solution of the approximated model. Finally, problems with discontinuous control profiles can be treated by introducing an extra level of elements (superelements) as decisions in the optimization problem. This approach is demonstrated on a simple optimal control problem as well as a reactor optimization problem with steep temperature profiles and state variable constraints.
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Cites
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Bryson, A. E., & Ho, Y.-C. (2018) · Routledge eBooks · doi:10.1201/9781315137667 · Cited by 6,015
The Method of Weighted Residuals and Variational Principles
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A fast algorithm for nonlinearly constrained optimization calculations
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Solution of boundary-value problems by orthogonal collocation
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Cited by
Dynamic flux balance analysis of diauxic growth in Escherichia coli
Mahadevan, R., Edwards, J. S., & Doyle, F. J. (2002) · Biophysical Journal · doi:10.1016/s0006-3495(02)73903-9 · Cited by 945
Biegler, L. T., & Grossmann, I. E. (2004) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2003.11.003 · Cited by 593
Self-citationVassiliadis, V. S., Sargent, R. W. H., & Pantelides, C. C. (1994) · Industrial & Engineering Chemistry Research · doi:10.1021/ie00033a014 · Cited by 530
Leibman, M. J., Edgar, T. F., & Lasdon, L. S. (1992) · Computers & Chemical Engineering · doi:10.1016/0098-1354(92)80030-d · Cited by 258
Global optimization for the parameter estimation of differential-algebraic systems
Esposito, W. R., & Floudas, C. A. (2000) · Industrial & Engineering Chemistry Research · doi:10.1021/ie990486w · Cited by 188
Metadata
- Authors
- Cuthrell, J. E., & Biegler, L. T.
- Venue
- AIChE Journal
- Publisher
- Wiley
- Published
- 1987-08
- Volume
- 33
- Issue
- 8
- Pages
- 1257-1270
- ISSN
- 0001-1541 (ISSN-L)
- 1547-5905
- OpenAlex
- W2113706446
- Cited by
- 450
- References
- 12
- FWCI
- 13.20
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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