Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation

Applied Numerical Mathematics

Volumn 48, Issue 1, 2004, Pages 83-102

  Schlegel, Martin ^a   Marquardt, Wolfgang ^a   Ehrig, Rainald ^b   Nowak, Ulrich ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

Differential algebraic systems; Dynamic optimization; Extrapolation methods; Optimal control; Sensitivity evaluation

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS; EXTRAPOLATION; OPTIMAL CONTROL SYSTEMS; SENSITIVITY ANALYSIS;

DIFFERENTIAL -ALGEBRAIC SYSTEMS (DAE); DYNAMIC OPTIMIZATION;

ALGEBRA;

EID: 0347985395     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2003.07.001     Document Type: Article

References (23)

1. D. Augustin, H. Maurer, Second order sufficient conditions and sensitivity analysis for the optimal control of a container crane under state constraints, Technical Report 00-17, Westfälische Wilhelms-Universität, Münster, 2000.
2. Betts J.T. Practical Methods for Optimal Control Using Nonlinear Programming. 2001;SIAM, Philadelphia, PA.
3. Bloss K.F., Biegler L.T., Schiesser W.E. Dynamic process optimization through adjoint formulation and constraint aggregation. Ind. Engrg. Chem. Res. 38:1999;421-432.
4. Brenan K.E., Campbell S.L., Petzold L.R. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. Classics Appl. Math. Vol. 14:1996;SIAM, Philadelphia, PA.
5. Bryson A.E., Ho Y.-C. Applied Optimal Control. 1975;Hemisphere, Bristol, PA.
6. Caracotsios M., Stewart W.E. Sensitivity analysis of initial value problems with mixed ODEs and algebraic equations. Comput. Chem. Engrg. 9:(4):1985;359-365.
7. Cervantes A., Biegler L.T. Large-scale DAE optimization using a simultaneous NLP formulation. AIChE J. 44:(5):1998;1038-1050.
8. Deuflhard P. Order and stepsize control in extrapolation methods. Numer. Math. (41). 1983;399-422.
9. Deuflhard P., Bornemann F. Numerische Mathematik II. 1994;de Gruyter, Berlin.
10. Deuflhard P., Hairer E., Zugck J. One-step and extrapolation methods for differential-algebraic systems. Numer. Math. (51). 1987;501-516.
11. Deuflhard P., Nowak U. Extrapolation integrators for quasilinear implicit odes. Deuflhard P., Enquist B. Large Scale Scientific Computing. NATO-ASI Series. 1987;37-50 Birkhäuser, Basel.
12. Deuflhard P., Nowak U., Wulkow M. Recent developments in chemical computing. Comput. Chem. Engrg. 14:(11):1990;1249-1258.
13. R. Ehrig, U. Nowak, P. Deuflhard, Highly scalable parallel linearly-implicit extrapolation algorithms, Technical Report TR 96-11, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, 1996.
14. Feehery W., Tolsma J., Barton P.I. Efficient sensitivity analysis of large-scale differential-algebraic systems. Appl. Numer. Math. 25:1997;41-54.
15. Hairer E., Norsett S.P., Wanner G. Solving Ordinary Differential Equations I, Nonstiff Problems. Springer Ser. Comput. Math. Vol. 8:1993;Springer, Berlin.
16. Kraft D. On converting optimal control problems into nonlinear programming problems. Comput. Math. Prog. 15:1985;261-280.
17. S. Li, L. Petzold, Design of new DDASPK for sensitivity analysis, Technical Report, Dept. of Mech. and Env. Engrg., University of California, Santa Barbara, CA, 1999.
18. Li S., Petzold L., Zhu W. Sensitivity analysis of differential-algebraic equations: A comparison of methods on a special problem. Appl. Numer. Math. 32:2000;161-174.
19. Maly T., Petzold L. Numerical methods and software for sensitivity analysis of differential-algebraic systems. Appl. Numer. Math. 20:1996.
20. Nowak U. Dynamic sparsing in stiff extrapolation methods. IMPACT Comput. Sci. Engrg. (5). 1993;53-74.
21. Schlegel M., Binder Th., Cruse A., Oldenburg J., Marquardt W. Component-based implementation of a dynamic optimization algorithm using adaptive parameterization. Gani R., Jørgensen S.B. European Symposium on Computer Aided Process Engineering-11. 2001;1071-1076 Elsevier, Amsterdam.
22. Støren S., Hertzberg T. Obtaining sensitivity information in dynamic optimization problems solved by the sequential approach. Comput. Chem. Engrg. 23:1999;807-819.
23. Vassiliadis V.S., Sargent R.W.H., Pantelides C.C. Solution of a class of multistage dynamic optimization problems: 1. Problems without path constraints. Ind. Engrg. Chem. Res. 33:(9):1994;2111-2122.