Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Singular Trajectories in Optimal Control

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_49-1


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.


End-point mapping Abnormal extremals Pseudo-Hamiltonian Saturation problem in NMR Martinet flat case in SR geometry 
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© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Institute of Mathematics, University of BurgundyDijonFrance