Switching time optimization in discretized hybrid dynamical systems

Kathrin Flasskamp*, Todd Murphey, Sina Ober-Blobaum

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

12 Scopus citations


Switching time optimization (STO) arises in systems that have a finite set of control modes, where a particular mode can be chosen to govern the system evolution at any given time. The STO problem has been extensively studied for switched systems that consists of time continuous ordinary differential equations with switching laws. However, it is rare that an STO problem can be solved analytically, leading to the use of numerical approximation using time discretized approximations of trajectories. Unlike the smooth optimal control problem, where differentiability of the discrete time control problem is inherited from the continuous time problem, in this contribution we show that the STO problem will in general be nondifferentiable in discrete time. Nevertheless, at times when it is differentiable the derivative can be computed using adjoint equations and when it is nondifferentiable the left and right derivatives can be computed using the same adjoint equation. We illustrate the results by a hybrid model of a double pendulum.

Original languageEnglish (US)
Article number6426414
Pages (from-to)707-712
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 2012
Event51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States
Duration: Dec 10 2012Dec 13 2012

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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