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Applied Mathematics and Optimization

, Volume 5, Issue 1, pp 231–252 | Cite as

Numerical computation of neighboring optimum feedback control schemes in real-time

  • Hans Josef Pesch
Article

Abstract

A modification of the theory of neighboring extremals is presented which leads to a new formulation of a linear boundary value problem for the perturbation of the state and adjoint variables around a reference trajectory. On the basis of the multiple shooting algorithm, a numerical method for stable and efficient computation of perturbation feedback schemes is developed. This method is then applied to guidance problems in astronautics. Using as much stored a priori information about the precalculated flight path as possible, the only computational work to be done on the board computer for the computation of a regenerated optimal control program is a single integration of the state differential equations and the solution of a few small systems of linear equations. The amount of computation is small enough to be carried through on modern board computers for real-time. Nevertheless, the controllability region is large enough to compensate realistic flight disturbances, so that optimality is preserved.

Keywords

Multiple Shooting Flight Path Reference Trajectory Feedback Scheme Optimum Feedback 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Hans Josef Pesch
    • 1
  1. 1.Institut für MathematikTechnischen Universität MünchenMünchen 2Federal Republic of Germany

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