SHOOT2.0: An indirect grid shooting package for optimal control problems, with switching handling and embedded continuation

Report English OPEN
Martinon , Pierre ; Gergaud , Joseph (2010)
  • Publisher: HAL CCSD
  • Subject: [ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]

The SHOOT2.0 package implements an indirect shooting method for optimal control problems. It is specifically designed to handle control discontinuities, with an automatic switching detection that requires no assumptions concerning the number of switchings. Special care is also devoted to the computation of the Jacobian matrix of the shooting function, using the variational system instead of classical finite differences. The package also features an embedded continuation method and an automatic (parallel) grid shooting in order to reduce the dependency to the initialization.
  • References (12)
    12 references, page 1 of 2

    [1] E. Allgower and K. Georg. Numerical Continuation Methods . Springer-Verlag, Berlin, 1990.

    [2] H.G. Bock. Numerical treatment of inverse problems in chemical reaction kinetics. In K.H. Ebert, P. Deuhard, and W. Jger, editors, Modelling of Chemical Reaction Systems, volume 18 of Springer Series in Chemical Physics , pages 102125. Springer, Heidelberg, 1981.

    [3] E. Cristiani and P. Martinon. Initialization of the shooting method via the hamilton-jacobi-bellman approach. Journal of Optimization Theory and Applications, 146(2):321346, 2010.

    [4] B.S. Garbow, K.E. Hillstrom, and J.J. More. User Guide for Minpack-1. National Argonne Laboratory, Illinois, 1980.

    [5] J. Gergaud and T. Haberkorn. Homotopy method for minimum consumption orbit transfer problem. Control, Optimization and Calculus of Variations , 12(2):294 310, 2006.

    [6] J. Gergaud, T. Haberkorn, and P. Martinon. Low thrust minimum-fuel orbital transfer: an homotopic approach. Journal of Guidance, Control and Dynamics , 27(6):10461060, 2004.

    [7] J. Gergaud and P. Martinon. Using switching detection and variational equations for the shooting method. Optimal Control Applications and Methods , 28(2):95 116, 2007.

    [8] T. Haberkorn. Transfert orbital poussØe faible avec minimisation de la consommation : rØsolution par homotopie diØrentielle . PhD thesis, INP Toulouse, 2004.

    [9] E. Hairer, S. P. Nłrsett, and G. Wanner. Solving ordinary dierential equations. I, volume 8 of Springer Series in Computational Mathematics . Springer-Verlag, Berlin, 1993.

    [10] R. Mannshardt. One-step methods of any order for odes with discontinuous rhs. Numer. Math., 31:131152, 1978.

  • Metrics
    No metrics available
Share - Bookmark