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

Ringkamp M, Ober-Blöbaum S, Leyendecker S (2016)

Publication Language: English

Publication Type: Book chapter / Article in edited volumes

Publication year: 2016

Publisher: Springer Berlin Heidelberg

Edited Volumes: Mathematical Programming

Pages Range: 1-31

DOI: 10.1007/s10107-016-1023-5

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.

Authors with CRIS profile

Maik Ringkamp Institute of Applied Dynamics Sigrid Leyendecker Institute of Applied Dynamics

Related research project(s)

Multiobjective optimal control of hybrid systems Jan. 1, 2012 - Jan. 1, 2016 Simulation and optimal control of the dynamics of multibody systems in biomechanics and robotics Dec. 1, 2008 - Dec. 1, 2011

Involved external institutions

University of Oxford GB United Kingdom (GB)

How to cite

APA:

Ringkamp, M., Ober-Blöbaum, S., & Leyendecker, S. (2016). On the time transformation of mixed integer optimal control problems using a consistent fixed integer control function. In Mathematical Programming. (pp. 1-31). Springer Berlin Heidelberg.

MLA:

Ringkamp, Maik, Sina Ober-Blöbaum, and Sigrid Leyendecker. "On the time transformation of mixed integer optimal control problems using a consistent fixed integer control function." Mathematical Programming. Springer Berlin Heidelberg, 2016. 1-31.

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