Integrated User Environment for the Numerical Solution of Optimal Control Problems

  • R. Mehlhorn
  • G. Sachs
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 8)


The paper starts explaining the motivation for realizing a new user environment for numerical solution of optimal control problems. After specification of the problem class addressed, the traditional process of solving these problems is shortly described. A modification of this process is derived, where the documentation of the optimization problem is used as an entry point. The modules of the integrated user environment and their tasks are denoted. An essential part of the user environment is the automatic transformation from documentation in LATEX to FORTRAN subroutines. An overview of the underlying concept is given and some results on the efficiency are provided. The appendix shows an example for application of the transparent programming concept.


Optimal Control Problem Adjoint System Automatic Differentiation Algebraic Condition User Environment 
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  1. 1.
    Mehlhorn, R., Lesch, K., Sachs, G.: A Technique for Improving Numerical Stability and Efficiency in Singular Control Problems. In AIAA Guidance, Navigation and Control Conference Proceedings, pages 388-396, August 1993. Number AIAA-93-3745-CPGoogle Scholar
  2. 2.
    Eich, E., Mehlhorn, R., Sachs, G.: Stabilization of Numerical Solutions of Boundary Value Problems Exploiting Invariants. In AIAA Guidance, Navigation and Control Conference Proceedings, 1994. Number AIAA-94-3580-CPGoogle Scholar
  3. 3.
    Sachs, G., Mehlhorn, R., Dinkelmann, M.: Flight Path Optimization Problems Related to Vehicle Fixed Thrust Direction. In AIAA Guidance, Navigation and Control Conference Proceedings, 1996. Number AIAA-96-3869Google Scholar
  4. 4.
    Bulirsch, R.: Die Mehrzielmethode zur numerischen Lösung von nichtlinearen Randwertproblemen und Aufgaben der optimalen Steuerung. Lehrgangsunterlagen, Carl-Cranz-Gesellschaft, Heidelberg, 1971, Nachdruck: Mathematisches Institut, Technische Universität München 1993Google Scholar
  5. 5.
    Hiltmann, P.: A Multiple Shooting Algoritm for Multipoint Boundary Value Problems. Technical Report 17, Lehrstuhl fur Hohere und Numerische Mathematik, München, 1994Google Scholar
  6. 6.
    Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F.:The Mathematical Theory of Optimal Processes. Interscience Publishers, New York, 1962zbMATHGoogle Scholar
  7. 7.
    Griewank, A.: Mathematical Programming: On Automatic Differentiation in Mathematical Programming - Recent Developements and Applications. Kluwer Academic Publishers, Boston, 1989Google Scholar
  8. 8.
    Kiehl, M., Mehlhorn, R., Schumann, M.: Parallel Multiple Shooting for Optimal Control Problems under NX. Optimization Methods and Software, 4:259–271, 1995CrossRefGoogle Scholar
  9. 9.
    Schumann, M., Lamberts, S., Stellner, G., Kiehl, M., Mehlhorn, R., Ludwig, T., Bode, A.: Parallel multiple shooting on Paragon XP/S, iPSC/860, and clusters of workstations: Aims, porting efforts and performance evaluation. In Proceedings of the Intel Supercomputer Users Group, 1994 Annual North America Users Conference, June 26-29, San Diego, Ca., pages 90-97, 1994Google Scholar
  10. 10.
    Schumann, M., Mehlhorn, R.: Exploiting HPC Architectures to Solve Optimal Control Problems. In A. Tentner, editor, High Performance Computing 1995 “Grand Challenges in Computer Simulation”, Proceedings of the 1995 Simulation Multiconference, Phoenix, AR, pages 323-328. The Society for Computer Simulation (SCS), Simulation Councils, Inc., April 9-13 1995. ISBN 1-56555-078-1Google Scholar
  11. 11.
    Lamport, L.: LATEX - A Document Preparation System. Addison-Wesley Publishing Company, Reading, Massachusetts, 1985Google Scholar
  12. 12.
    Bryson, A.E., Ho, Y.C.: Applied Optimal Control. Hemisphere Publishing Corporation, Washington, 1975Google Scholar
  13. 13.
    Mehlhorn, R.: Integrierte Arbeitsumgebung zur numerischen Berechnung von Problemen der optimalen Steuerung. Herbert Utz Verlag, München, 1996. ISBN 3–89675-111-5Google Scholar
  14. 14.
    Humphrey, W. S.: A Discipline for Software Engineering. Addison-Wesley Publishing Company, 1995Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • R. Mehlhorn
    • 1
  • G. Sachs
    • 2
  1. 1.Tecoplan Informatik GmbHOttobrunn/MünchenGermany
  2. 2.Lehrstuhl fur Flugmechanik und FlugregelungTechnische Universitat MünchenGarching/MünchenGermany

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