Towards hybrid optimal control

At-Automatisierungstechnik

Volumn 48, Issue 9, 2000, Pages 448-1459

  Buss, Martin ^a   Von Stryk, Oskar ^a   Bulirsch, Roland ^a   Schmidt, Günther ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85006820930     PISSN: 01782312     EISSN: None     Source Type: Journal    
DOI: 10.1524/auto.2000.48.9.448     Document Type: Article

References (35)

1. C. S. Adjiman, C. A. Schweiger, C. A. Floudas. Mixed-integer nonlinear optimization in process synthesis. In D.-Z. Du, P. M. Pardalos, editors, Handbook of Combinatorial Optimization, Kluwer Academic Publishers, 1999.
2. A. Barclay, P. E. Gill, J. B. Rosen. SQP methods and their application to numerical optimal control. In W. H. Schmidt, K. Heier, L. Bittner, R. Bulirsch, editors, Variational Calculus, Optimal Control and Application, International Series of Numerical Mathematics 124, pp. 207-222, Birkhäuser, Basel, 1998.
3. J. T. Betts. Survey of numerical methods for trajectory optimization. AIAA J. Guidance, Control, and Dynamics 21(2): 193-207, 1998.
4. M. S. Branicky, V. S. Borkar, S. K. Mitter. A unified framework for hybrid control: model and optimal control theory. IEEE Transactions on Automatic Control, 43(1): 31-45, January 1998.
5. M. H. Breitner. Real-time capable approximation of optimal strategies in complex differential games. In M. Breton, G. Zaccour, editors, Proceedings of the Sixth International Symposium on Dynamic Games and Applications, St.-Jovite, Quebec, CAN, July 13-15, Ecole des Hautes Etudes Commerciales, Montreal, pp. 370-384, 1994.
6. M. H. Breitner. Robust optimal on-board reentry guidance of a space shuttle: dynamic game approach and guidance synthesis with neural networks. J. Optimization Theory and Applications, to appear, 2000/2001.
7. A. E. Bryson and Y.-C. Ho. Applied Optimal Control. Ginn, Waltham, MA, 1969.
8. R. Bulirsch. Die Mehrzielmethode zur numerischen Lösung von nichtlinearen Randwertproblemen und Aufgaben der optimalen Steuerung. Report of the Carl-Cranz-Gesellschaft e.V., DLR, Oberpfaffenhofen, 1971.
9. R. Bulirsch, K. Chudej. Combined optimization of trajectory and stage separation of a hypersonic two-stage space vehicle. Z Flugwiss. Weltraumforsch. 19: 55-60, 1995.
10. S. Engell. Modellierung und Analyse hybrider dynamischer Systeme. at-Automatisierungstechnik, 45(4): 152-162, 1997.
11. P. E. Gill, W. Murray, M. A. Saunders. SNOPT: An SQP algorithm for large-scale constrained optimization. Report NA 972, Department of Mathematics, University of California, San Diego, 1997.
12. I. E. Grossmann, Z. Kravanja. Mixed-integer nonlinear programming: a survey of algorithms and applications. In: L. T. Biegler, T. F. Coleman, A. R. Conn, F. N. Santosa, editors, Large-Scale Optimization with Applications, Part II, pp. 73-100, Springer, 1997.
13. C. R. Hargraves, S. W. Paris. Direct trajectory optimization using nonlinear programming and collocation. AIAA J. Guidance 10(4): 338-342, 1987.
14. R. F. Hartl, S. P. Sethi, R. G. Vickson. A survey of the Maximum Principles for optimal control problems with state constraints. SIAM Review 37(2): 181-218, 1995.
15. S. Hedlund and A. Rantzer. Optimal control of hybrid systems. In Proceedings of the 38th IEEE Conference on Decision and Control, pp. 3972-3977, Phoenix, AZ, 1999.
16. W. Kohn and J. B. Remmel. Hybrid dynamic programming. In O. Maler, editor, Lecture Notes in Computer Science 1201; Hybrid and Real-Time Systems, Proceedings of the International Workshop HART’97, pp. 391-396, Springer, 1997.
17. G. Labinaz, M. M. Bayoumi, K. Rudie. Modeling and control of hybrid systems: a survey. In J. J. Gertler, J. B. Cruz, M. Peshkin, editors, Preprints of the 13th World Congress, volume C, pp. 293-304, International Federation of Automatic Control-IFAC, San Francisco, 1996.
18. E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, D. B. Shmoys, editors. The Traveling Salesman Problem. Chiche-ster: John Wiley & Sons, Chichester, 1985.
19. J. Mareczek, M. Buss, G. Schmidt. Robust control of a non-holonomic underactuated SCARA robot. In S. G. Tzafestas and G. Schmidt, editors, Progress in System and Robot Analysis and Control Design), volume 243 of Lecture Notes in Control and Information Sciences, pp. 381-396, Springer, 1999.
20. J. Mareczek, M. Buss, G. Schmidt. Robuste Regelung eines nicht-holonomen, unteraktuierten SCARA Roboters. at-Auto-matisierungstechnik, 47(5): 199-208, Mai 1999.
21. G. Nenninger, M. Schnabel, V. Krebs. Modellierung, Simulation und Analyse hybrider dynamischer Systeme mit Netz-Zu-stands-Modellen. at-Automatisierungstechnik, 47(3): 118-126, März 1999.
22. H. J. Pesch. A practical guide to the solution of real-life optimal control problems. Control and Cybernetics 23: 7-60, 1994.
23. H. J. Pesch, R. Bulirsch. The Maximum Principle, Bellman’s Equation, and Caratheodory’s Work. J. Optimization Theory and Applications 80(2): 199-225, 1994.
24. B. Piccoli. Necessary conditions for hybrid optimization. In Proceedings of the 38th IEEE Conference on Decision and Control, pp. 410-415, Phoenix, AZ, 1999.
25. L. S. Pontryagin, V. G. Boltyanski, R. V. Gamkrelidze, E. F. Miscenko. The Mathematical Theory of Optimal Processes. Wiley, New York, 1962.
26. T. Schlegl, M. K. Schnabel, M. Buss, V. Krebs, G. Schmidt. Zustandsrekonstruktion und Fehlerkompensation in diskretkontinuierlichen Systemen. at-Automatisierungstechnik, 48, 2000.
27. M. W. Spong. Some aspects of switching control in robot locomotion. at-Automatisierungstechnik, 48(4): 157-164, April 2000.
28. J. Stoer, R. Bulirsch. Introduction to Numerical Analysis. 2nd ed., Springer-Verlag, 1993.
29. H. J. Sussmann. A maximum principle for hybrid optimal control problems. In Proceedings of the 38th IEEE Conference on Decision and Control, pp. 425-430, Phoenix, AZ, 1999.
30. O. von Stryk. Numerische Lösung optimaler Steuerungsprobleme: Diskretisierung, Parameteroptimierung und Berechnung der adjungierten Variablen. Fortschritt-Berichte VDI, Reihe 8, Nr. 441, VDI-Verlag, Düsseldorf, 1995.
31. O. von Stryk. User’s Guide for DIRCOL Version 2.1: A direct collocation method for the numerical solution of optimal control problems. Report, Lehrstuhl M2 Höhere Mathematik und Numerische Mathematik, Technische Universität München, November 1999.
32. O. von Stryk. Numerical hybrid optimal control. Habilitationsschrift, Technische Universität München, submitted.
33. O. von Stryk, R. Bulirsch. Direct and indirect methods for trajectory optimization. Annals of Operations Research 37: 357-373, 1992.
34. O. von Stryk, M. Glocker. Decomposition of mixed-integer optimal control problems using branch and bound and sparse direct collocation. In Proceedings of ADPM 2000-Automation of Mixed Processes: Hybrid Dynamic Systems, Dortmund, September 18-19, 2000.
35. H. Tolle. Optimization Methods. Berlin, New York, Springer Verlag, 1975.