Geodesic
Geometry of neighborhoods of singular trajectories in problems with multidimensional control
Informatics and Automation, Mathematical control theory and differential equations, Tome 277 (2012), pp. 74-90.

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It is shown that the order of a singular trajectory in problems with multidimensional control is described by a flag of linear subspaces in the control space. In terms of this flag, we construct necessary conditions for the junction of a nonsingular trajectory with a singular one in affine control systems. We also give examples of multidimensional problems in which the optimal control has the form of an irrational winding of a torus that is passed in finite time. 
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M. I. Zelikin; L. V. Lokutsievskiy; R. Hildebrand. Geometry of neighborhoods of singular trajectories in problems with multidimensional control. Informatics and Automation, Mathematical control theory and differential equations, Tome 277 (2012), pp. 74-90. http://geodesic.mathdoc.fr/item/TRSPY_2012_277_a5/

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