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Fast Linear Algebra for Multiarc Trajectory Optimization

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Large-Scale Nonlinear Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 83))

Summary

This paper presents some methods for solving in a fast and reliable way the linear systems arising when solving an optimal control problem by a Runge-Kutta discretization scheme, combined with an interior-point algorithm. Our analysis holds for a multiarc problem, i.e., when several arcs, each of them associated with a dynamics and integral cost, are linked by junction points, called nodes; with the latter are associated junction conditions and a cost function.

Our main result is that a sparse QR band factorization combined with a specific elimination procedure for arcs and nodes allows to factorize the Jacobian of the discrete optimality system in a small number of operations. Combined with an “optimal” refinement procedure, this gives an efficient method that we illustrate on Goddard’s problem.

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References

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Author information

Authors and Affiliations

  1. Long-Term Design & System Integration Department, ONERA, BP 72, 29 av. division Leclerc, 92322, Châtillon, France

    Nicolas Bérend

  2. Projet Sydoco INRIA, B.P. 105, 78153, Le Chesnay, France

    J. Frédéric Bonnans & Julien Laurent-Varin

  3. Long-Term Design & System Integration Department, ONERA, France

    Julien Laurent-Varin

  4. UMR 6628, MAPMO, BP 6759, 45067, Orléans Cedex 2, France

    Mounir Haddou

  5. Launcher Directorate, CNES, Rond-Point de l’Espace, 91023, Evry Cedex, France

    Christophe Talbot

Authors
  1. Nicolas Bérend
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  2. J. Frédéric Bonnans
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  3. Julien Laurent-Varin
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  4. Mounir Haddou
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  5. Christophe Talbot
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Editor information

Editors and Affiliations

  1. University of Rome “La Sapienza”, Italy

    G. Di Pillo  & M. Roma  & 

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© 2006 Springer Science+Business Media, Inc.

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Bérend, N., Bonnans, J.F., Laurent-Varin, J., Haddou, M., Talbot, C. (2006). Fast Linear Algebra for Multiarc Trajectory Optimization. In: Di Pillo, G., Roma, M. (eds) Large-Scale Nonlinear Optimization. Nonconvex Optimization and Its Applications, vol 83. Springer, Boston, MA. https://doi.org/10.1007/0-387-30065-1_1

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