Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Singular Trajectories in Optimal Control

  • Bernard BonnardEmail author
  • Monique Chyba
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_49


Singular trajectories arise in optimal control as singularities of the end-point mapping. Their importance has long been recognized, at first in the Lagrange problem in the calculus of variations where they are lifted into abnormal extremals. Singular trajectories are candidates as minimizers for the time-optimal control problem, and they are parameterized by the maximum principle via a pseudo-Hamiltonian function. Moreover, besides their importance in optimal control theory, these trajectories play an important role in the classification of systems for the action of the feedback group.


Abnormal extremals End-point mapping Martinet flat case in sub-Riemannian geometry Pseudo-Hamiltonian 
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© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of BurgundyDijonFrance
  2. 2.University of Hawaii-ManoaManoaUSA