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On the Convexification of Optimal Control Problems of Flight Dynamics

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Variational Calculus, Optimal Control and Applications

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 124))

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Abstract

The control structure of the differential equations of a typical flight dynamical control problem is studied and methods for defining a relaxed problem with the aid of a least number of additional control parameters are presented. The usefulness of the relaxed problems for proving the existence of optimal solutions and calculating approximately optimal solutions is explained in detail.

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References

  1. Bittner, L.: Zur Existenz von Optimallösungen für das Problem des Wiedereintritts in die Atmosphäre und das Problem des Einschwenkens in eine Umlaufbahn. Rep. Nr. 20 des Sonderforschungsbereichs (SFB) 255 der DFG, 1994.

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  2. Bittner, L.: Zur Existenz einer optimalen Lösung des Brachistochroneproblems mit Tangentialwinkelbeschränkungen. Rep. Nr. 29 des SFB 255 der DFG, 1995.

    Google Scholar 

  3. Bittner, L.: Zur Konvexifizierung von Optimalsteuerproblemen. Rep. Nr. 33 des SFB 255 der DFG, 1996.

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  4. Bulirsch, R.; Chudej, K.: Combined optimization of trajectory and stage separation of a hypersonic two-stage space vehicle. Z. Flugwiss. Weltraumforschung 19 (1995) 55–60.

    Google Scholar 

  5. Butzek, S.; Schmidt, W.: Konstruktion von Näherungslösungen für Steuerprobleme mit Hilfe von Lösungen relaxierter Probleme. Rep. Nr. 26 des SFB 255 der DFG, 1996.

    Google Scholar 

  6. Dunford, N.; Schwartz, J. T.: Linear Operators I. Interscience Publishers, New York, 1958.

    MATH  Google Scholar 

  7. Lee, E. B.; Marcus, L.: Foundations of Optimal Control Theory. John Wiley Inc., New York, 1970.

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  8. Macky, P.; Strauss, A.: Introduction to Optimal Control Theory. Springer, Berlin, 1988.

    Google Scholar 

  9. Sachs, G.; Mehlhorn, R.; Dinkelmann, N.: Efficient convexification of flight path optimization problems. This volume.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität Greifswald, Jahnstr. 15a, D-17487, Greifswald, Germany

    Leonhard Bittner

Authors
  1. Leonhard Bittner
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Editor information

Editors and Affiliations

  1. Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität Greifswald, Jahnstr. 15a, D-17487, Greifswald, Germany

    Werner H. Schmidt , Knut Heier  & Leonhard Bittner ,  & 

  2. Zentrum Mathematik, Technische Universität München, Arcisstr. 21, D-80290, München, Germany

    Roland Bulirsch

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Bittner, L. (1998). On the Convexification of Optimal Control Problems of Flight Dynamics. In: Schmidt, W.H., Heier, K., Bittner, L., Bulirsch, R. (eds) Variational Calculus, Optimal Control and Applications. International Series of Numerical Mathematics, vol 124. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8802-8_1

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  • DOI: https://doi.org/10.1007/978-3-0348-8802-8_1

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9780-8

  • Online ISBN: 978-3-0348-8802-8

  • eBook Packages: Springer Book Archive

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