Geodesic
Chattering regimes and Lagrangian manifolds in problems with phase constraints
Izvestiya. Mathematics , Tome 76 (2012) no. 1, pp. 1-38

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Given a class of optimal control problems with a phase constraint, we construct a Lagrangian manifold containing extremals with countably many tangencies to the boundary of that constraint. The construction proceeds by resolving the singularities of the Hamiltonian system of the problem at the accumulation point of the points of contact of extremals with that boundary.
Keywords: phase constraints, Pontryagin's maximum principle, Lagrangian manifolds, chattering regimes, blow up. 
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     author = {V. F. Borisov and V. V. Gael and M. I. Zelikin},
     title = {Chattering regimes and {Lagrangian} manifolds in problems with phase constraints},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_1_a0/}
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V. F. Borisov; V. V. Gael; M. I. Zelikin. Chattering regimes and Lagrangian manifolds in problems with phase constraints. Izvestiya. Mathematics , Tome 76 (2012) no. 1, pp. 1-38. http://geodesic.mathdoc.fr/item/IM2_2012_76_1_a0/