Discretized switching time optimization problems

Kathrin Flasskamp, Todd David Murphey, Sina Ober-Blobaum

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


A switched system is defined by a family of vector fields together with a switching law which chooses the active vector field at any time. Thus, the switching law encoding the switching times and the sequence of modes may serve as a design parameter. Switching time optimization (STO) focuses on the optimization of the switching times in order to govern the system evolution to a desired behavior described by some cost function. However, it is rare that a STO problem can be solved analytically leading to the use of numerical approximation methods. In this contribution, we directly start with applying integration schemes to approximate the system's state and adjoint trajectories and study the effect of this discretization. It turns out that in contrast to the continuous time problem, the discretized problem loses differentiability with respect to the optimization variables. The isolated nondifferentiable points can be precisely identified though. Nevertheless, to solve the STO problem, nonsmooth optimization techniques have to be applied which we illustrate using a hybrid double pendulum.

Original languageEnglish (US)
Title of host publication2013 European Control Conference, ECC 2013
Number of pages6
StatePublished - Dec 1 2013
Event2013 12th European Control Conference, ECC 2013 - Zurich, Switzerland
Duration: Jul 17 2013Jul 19 2013

Publication series

Name2013 European Control Conference, ECC 2013


Other2013 12th European Control Conference, ECC 2013

ASJC Scopus subject areas

  • Control and Systems Engineering

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