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On the time transformation of mixed integer optimal control problems using a consistent fixed integer control function

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Abstract

Nonlinear control systems with instantly changing dynamical behavior can be modeled by introducing an additional control function that is integer valued in contrast to a control function that is allowed to have continuous values. The discretization of a mixed integer optimal control problem (MIOCP) leads to a non differentiable optimization problem and the non differentiability is caused by the integer values. The paper is about a time transformation method that is used to transform a MIOCP with integer dependent constraints into an ordinary optimal control problem. Differentiability is achieved by replacing a variable integer control function with a fixed integer control function and a variable time allows to change the sequence of active integer values. In contrast to other contributions, so called control consistent fixed integer control functions are taken into account here. It is shown that these control consistent fixed integer control functions allow a better accuracy in the resulting trajectories, in particular in the computed switching times. The method is verified on analytical and numerical examples.

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Acknowledgments

The authors would like to thank the anonymous reviewers for helpful comments and suggestions.

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Authors and Affiliations

  1. Chair of Applied Dynamics, University of Erlangen-Nuremberg, Haberstrasse 1, 91058, Erlangen, Germany

    Maik Ringkamp & Sigrid Leyendecker

  2. Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK

    Sina Ober-Blöbaum

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  1. Maik Ringkamp
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Correspondence to Maik Ringkamp.

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Ringkamp, M., Ober-Blöbaum, S. & Leyendecker, S. On the time transformation of mixed integer optimal control problems using a consistent fixed integer control function. Math. Program. 161, 551–581 (2017). https://doi.org/10.1007/s10107-016-1023-5

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