Nonlinear Dynamics

, Volume 70, Issue 2, pp 1523–1534 | Cite as

OGY method for a class of discontinuous dynamical systems

  • Marius-F. Danca
Original Paper


In this paper, we prove that the OGY method to control unstable periodic orbits (UPOs) of continuous-time systems can be applied to a class of systems discontinuous with respect the state variable, by using a generalized derivative. Because the discontinuous problem may have not classical solutions, the initial value problem is transformed into a set-valued problem via Filippov regularization. The existence of the ingredients necessary to apply OGY method (UPO, Poincaré map and stable and unstable directions) is proved and the numerically implementation is explained. Another possible way analyzed in this paper is the continuous approximation of the underlying initial value problem, via Cellina’s theorem for differential inclusions. Thus, the problem is approximated by a continuous initial value problem, and the OGY method can be applied as usual.


Generalized derivative OGY method Poincaré map Filippov regularization Cellina’s theorem 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Dept. of Mathematics and Computer ScienceAvram Iancu UniversityCluj-NapocaRomania
  2. 2.Romanian Institute of Science and TechnologyCluj-NapocaRomania

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