Abstract
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.
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Bonnard, B., Chyba, M. (2014). Singular Trajectories in Optimal Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_49-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_49-1
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