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1 results

  • Asymptotics of accessibility sets along anabnormal trajectory

  • Emmanuel Trélat
  • Journal:
    ESAIM: Control, Optimisation and Calculus of Variations / Volume 6 / 2001
    Published online by Cambridge University Press:
    15 August 2002, pp. 387-414
    Print publication:
    2001

  • We describe precisely, under generic conditions, the contact ofthe accessibility set at time T with an abnormal direction,first for a single-input affine control system with constraint onthe control, and then as anapplication for a sub-Riemannian system of rank 2. As aconsequence we obtain in sub-Riemannian geometry a newsplitting-up of the sphere near an abnormal minimizer γinto two sectors, bordered by the first Pontryagin's cone alongγ, called the L∞-sector and the L2-sector.Moreover we find again necessary and sufficient conditions ofoptimality of an abnormal trajectory for such systems,for any optimization problem.