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Instationary Heat-Constrained Trajectory Optimization of a Hypersonic Space Vehicle by ODE–PDE-Constrained Optimal Control

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Variational Analysis and Aerospace Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 33))

Abstract

During ascent and reentry of a hypersonic space vehicle into the atmosphere of any heavenly body, the space vehicle is subjected, among others, to extreme aerothermic loads. Therefore, an efficient, sophisticated and lightweight thermal protection system is determinative for the success of the entire mission. For a deeper understanding of the conductive, convective and radiative heating effects through a thermal protection system, a mathematical model is investigated which is given by an optimal control problem subject to not only the usual dynamic equations of motion and suitable control and state variable inequality constraints but also an instationary quasi-linear heat equation with nonlinear boundary conditions. By this model, the temperature of the heat shield can be limited in certain critical regions. The resulting ODE–PDE-constrained optimal control problem is solved by a second-order semi-discretization in space of the quasi-linear parabolic partial differential equation yielding a large-scale nonlinear ODE-constrained optimal control problem with additional state constraints for the heat load. Numerical results obtained by a direct collocation method are presented, which also include those for active cooling of the engine by the liquid hydrogen fuel. The aerothermic load and the fuel loss due to engine cooling can be considerably reduced by optimization.

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Author information

Authors and Affiliations

  1. Lehrstuhl für Ingenieurmathematik, Universität Bayreuth, Bayreuth, Germany

    Kurt Chudej & Hans Josef Pesch

  2. German Institute of Science and Technology, Singapore, Singapore

    Markus Wächter

  3. Lehrstuhl für Flugmechanik und Flugregelung, Technische Universität München, München, Germany

    Gottfried Sachs

  4. Laboratoire de Recherches Balistiques et Aérodynamiques, Délégation Générale pour l’Armement, formerly: École Polytechnique Paris, Vernon, France

    Florent Le Bras

Authors
  1. Kurt Chudej
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  2. Hans Josef Pesch
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  3. Markus Wächter
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  4. Gottfried Sachs
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  5. Florent Le Bras
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Corresponding author

Correspondence to Kurt Chudej .

Additional information

This contribution is dedicated to Professor Angelo Miele on the occasion of his 85th birthday.

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© 2009 Springer-Verlag New York

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Chudej, K., Pesch, H.J., Wächter, M., Sachs, G., Le Bras, F. (2009). Instationary Heat-Constrained Trajectory Optimization of a Hypersonic Space Vehicle by ODE–PDE-Constrained Optimal Control. In: Variational Analysis and Aerospace Engineering. Springer Optimization and Its Applications, vol 33. Springer, New York, NY. https://doi.org/10.1007/978-0-387-95857-6_8

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