Exploiting invariants in the numerical solution of multipoint boundary value problems for DAEs

SIAM Journal on Scientific Computing

Volumn 19, Issue 2, 1998, Pages 440-467

  Schulz, Volker H ^a   Bock, Hans Georg ^b   Steinbach, Marc C ^c  

^a UNIVERSITY OF STUTTGART   (Germany)

^b UNIVERSITY OF HEIDELBERG   (Germany)

^c ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

Boundary value problems; Descriptor form for multibody systems; Higher index differential algebraic equations; Invariants; Optimal control; Parameter identification; Singular control; State constraints

Indexed keywords

EID: 9144254129     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827594261917     Document Type: Article

References (35)

1. T. ALISHENAS, Zur numerischen Behandlung, Stabilisierung durch Projektion und Modellierung mechanischer Systeme mit Nebenbedingungen und Invarianten, Ph.D. thesis, Royal Institute of Technology, Stockholm, Sweden, 1992.
2. TH. ANDRZEJEWSKI, H. G. BOCK, E. EICH, AND R. VON SCHWERIN, Recent advances in the numerical integration of multibody systems, in Advanced Multibody System Dynamics, Simulation and Software Tools, W. Schiehlen, ed., Kluwer Academic Publishers, Dordrecht, Boston, London, 1993, pp. 127-151.
3. U. M. ASCHER, R. M. M. MATTHEIJ, AND R. D. RUSSELL, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1988.
4. U. M. ASCHER AND L. R. PETZOLD, Projected Collocation for Higher-Order Higher-Index Differential-Algebraic Equations, Technical report 91-9, Department of Computer Science, University of British Columbia, Vancouver, British Columbia, Canada, 1991.
5. U. M. ASCHER, H. QIN, AND S. REICH, Stabilization of DAEs and invariant manifolds, Numer. Math., 67 (1994), pp. 131-149.
6. U. M. ASCHER AND R. J. SPITERI, Collocation software for boundary value differential-algebraic equations, SIAM J. Sci. Comput., 15 (1994), pp. 938-952.
7. J. BAUMGARTE, Stabilization of constraints and integrals of motion in dynamical systems, Comput. Math. Appl. Mech. Engrg., 1 (1976), pp. 1-16.
8. H. G. BOCK, Numerische Behandlung von zustandsbeschränkten und Chebyshev-Steuerungs-problemen, Technical report, Carl-Cranz-Gesellschaft, Oberpfaffenhofen, Germany, 1981.
9. H. G. BOCK, Recent advances in parameter identification techniques for O.D.E., in Numerical Treatment of Inverse Problems, P. Deuflhard and E. Hairer, eds., Progress in Scientific Computing 2, Birkhäuser, Boston, 1983.
10. H. G. BOCK, Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen, Bonner Mathematische Schriften Nr. 183, University of Bonn, Bonn, Germany, 1987.
11. H. G. BOCK, E. EICH, AND J. P. SCHLÖDER, Numerical solution of constrained least squares boundary value problems in differential-algebraic equations, in Numerical Treatment of Differential Equations, K. Strehmel, ed., Teubner, Leipzig, Germany, 1988.
12. H. G. BOCK AND R. VON SCHWERIN, An Inverse Dynamics ADAMS-Method for Constrained Multibody Systems, Preprint 93-27, IWR, University of Heidelberg, Heidelberg, Germany, 1993.
13. K. E. BRENAN, S. L. CAMPBELL, AND L. R. PETZOLD, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, Amsterdam, 1989.
14. A. E. BRYSON, W. F. DENHAM, AND S. E. DREYFUS, Optimal programming problems with inequality constraints I, AIAA J., 1 (1963), pp. 2544-2550.
15. P. A. M. DIRAC, Lectures on Quantum Mechanics, Belfer Graduate School Monographs, No. 3, Yeshiva University, New York, 1964.
16. E. EICH, Projizierende Mehrschrittverfahren zur Numerischen Lösung von Bewegungsgleichungen Technischer Mehrkörpersysteme mit Zwangsbedingungen und Unstetigkeiten, Ph.D. thesis, University of Augsburg, Augsburg, Germany, 1991; Fortschritts-Berichte VDI, Reihe 18, Nr. 109, VDI-Verlag, Düsseldorf, Germany, 1992.
17. E. EICH, Projizierende Mehrschrittverfahren zur Numerischen Lösung von Bewegungsgleichungen Technischer Mehrkörpersysteme mit Zwangsbedingungen und Unstetigkeiten, Ph.D. thesis, University of Augsburg, Augsburg, Germany, 1991; Fortschritts-Berichte VDI, Reihe 18, Nr. 109, VDI-Verlag, Düsseldorf, Germany, 1992.
18. C. FÜHRER, Differential-algebraische Gleichungssysteme in mechanischen Mehrkörpersystemen, Ph.D. thesis, Munich University of Technology, München, Germany, 1988.
19. E. GRIEPENTROG AND R. MÄRZ, Differential-Algebraic Equations and Their Numerical Treatment, Teubner-Text Math., 88, Teubner, Leipzig, 1986.
20. A. GRIEWANK, On automatic differentiation, in Mathematical Programming: Recent Developments and Applications, M. Iri and K. Tanabe, eds., Kluwer Academic Publishers, Dordrecht, Boston, London, 1989, pp. 83-108.
21. F. GRUPP AND W. KORTÜM, Parameter identification of nonlinear descriptor systems, in Advanced Multibody System Dynamics, Simulation and Software Tools, W. Schiehlen, ed., Kluwer Academic Publishers, Dordrecht, Boston, London, 1993, pp. 457-462.
22. M. HANKE, On a least-squares collocation method for linear differential-algebraic equations, Numer. Math., 54 (1988), pp. 79-90.
23. F. R. DE HOOG AND R. M. M. MATTHEIJ, On dichotomy and well conditioning in BVP, SIAM J. Numer. Anal., 24 (1987), pp. 89-105.
24. H. J. KELLEY, R. E. KOPP, AND H. G. MOVER, Singular extremals, in Topics in Optimization, G. Leitmann, ed., Academic Press, New York, 1967.
25. R. LAMOUR, Shooting Methods for Transferable DAE's - Solution of Shooting Equation, Vol. XXIV, Banach Center Publications, Warsaw, Poland, 1990.
26. R. LAMOUR, A well-posed shooting method for transferable DAE's, Numer. Math., 59 (1991), pp. 815-829.
27. B. LEIMKUHLER AND S. REICH, Symplectic integration of constrained Hamiltonian systems, Math. Comp., 63 (1994), pp. 589-605.
28. M. LENTINI AND R. MÄRZ, The conditioning of boundary value problems in transferable differential-algebraic equations, SIAM J. Numer. Anal., 27 (1990), pp. 1001-1015.
29. M. LENTINI AND R. MÄRZ, Conditioning and dichotomy in differential algebraic equations, SIAM J. Numer. Anal., 27 (1990), pp. 1519-1526.
30. R. MÄRZ, On boundary value problems in differential-algebraic equations, Appl. Math. Comput., 31 (1989), pp. 517-537.
31. R. MEHLHORN, K. LESCH, AND G. SACHS, A technique for improving stability and efficiency in singular control problems, in Proc. 1993 AIAA Guidance, Navigation, and Control Conf., Monterey, CA, 1993.
32. G. SACHS AND K. LESCH, Periodic maximum range cruise with singular control, in Proc. 1990 AIAA Guidance, Navigation, and Control Conf., Portland, OR, 1990.
33. G. SACHS, K. LESCH, H. G. BOCK, AND M. STEINBACH, Periodic optimal trajectories with singular control for aircraft with high aerodynamic efficiency, in Optimal Control: Calculus of Variations, Optimal Control Theory and Numerical Methods, R. Bulirsch, A. Miele, J. Stoer, and K. H. Well, eds., International Series in Numerical Mathematics, 111, Birkhäuser, Basel, Boston, Berlin, 1993, pp. 289-304.
34. J. P. SCHLÖDER, Numerische Methoden zur Behandlung hochdimensionaler Aufgaben der Parameteridentifizierung, Bonner Mathematische Schriften Nr. 187, University of Bonn, Bonn, Germany, 1988.
35. V. SCHULZ, Ein effizientes Kollokationsverfahren zur numerischen Behandlung von Mehrpunktrandwertaufgaben in der Parameteridentifizierung und Optimalen Steuerung, Diploma thesis, University of Augsburg, Augsburg, Germany, 1990.