Discrete Event Dynamic Systems

, Volume 15, Issue 4, pp 433–448

Optimal Control of Switching Surfaces in Hybrid Dynamical Systems


DOI: 10.1007/s10626-005-4060-4

Cite this article as:
Boccadoro, M., Wardi, Y., Egerstedt, M. et al. Discrete Event Dyn Syst (2005) 15: 433. doi:10.1007/s10626-005-4060-4


This paper concerns an optimal control problem defined on a class of switched-mode hybrid dynamical systems. The system's mode is changed (switched) whenever the state variable crosses a certain surface in the state space, henceforth called a switching surface. These switching surfaces are parameterized by finite-dimensional vectors called the switching parameters. The optimal control problem is to minimize a cost functional, defined on the state trajectory, as a function of the switching parameters. The paper derives the gradient of the cost functional in a costate-based formula that reflects the special structure of hybrid systems. It then uses the formula in a gradient-descent algorithm for solving an obstacle-avoidance problem in robotics.


hybrid systemsswitching surfacesoptimal controlgradient descentobstacle avoidance

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • M. Boccadoro
    • 1
  • Y. Wardi
    • 2
  • M. Egerstedt
    • 2
  • E. Verriest
    • 2
  1. 1.Dipartimento di Ingegneria Elettronica e dell'InformazioneUniversità di PerugiaPerugiaItaly
  2. 2.School of Electrical and Computer EngineeringGeorgia Institute of TechnologyAtlantaUSA