Determining the Controllability Region for the Re-Entry of an Apollo-Type Spacecraft

  • Dietmar W. Tscharnuter
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 124)


In closed and open control loops, particularly in optimal control problems, the controllability region of the perturbations is a factor of importance. One looks for those controls which guarantee that the system stays within the controllability region: small perturbations must be compensated by suitable controlling in such a way that the controllability region is not left. In general, optimal control problems are characterized by a given quality functional, which has to be minimized, and by boundary conditions. Especially in closed optimal loops the terminal condition has to be fulfilled either exactly or within a prescribed neighborhood of the terminal point, when talking about real-time controlling. For the special problem of the atmospheric re-entry of an Apollo-type capsula the aim of this paper is to determine the controllability region and to characterize it by a manifold. This manifold will be constructed by methods of the stability theory, since the controllability region can be interpreted as a generalized epsilon-tube, where the nominal orbit that can be determined beforehand is flight-path stable. Some numerical results are presented.


Equilibrium Point Controllability Region Optimal Control Problem LYAPUNOV Function Terminal Condition 
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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Dietmar W. Tscharnuter
    • 1
  1. 1.Lehrstuhl für Höhere Mathematik und Numerische Mathematik — FORTWIHRTechnische Universität MünchenMünchenGermany

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