Geodesic
On an optimal flow in a class of nilpotent convex problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 291 (2015), pp. 157-181

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A comprehensive analysis of optimal synthesis is carried out for a class of nilpotent convex problems with multidimensional control. It is shown that the synthesis of optimal trajectories forms a nonsmooth half-flow (which is reasonably called optimal) in the state space. An optimal solution starting at some point of the state space is the trajectory of this point under the action of the optimal flow. The existence of an optimal flow entails many important corollaries. For example, applying the Cantor–Bendixson theorem, one can prove that an optimal control in nilpotent convex problems may have at most a countable number of discontinuity points. 
@article{TM_2015_291_a12,
     author = {L. V. Lokutsievskiy},
     title = {On an optimal flow in a class of nilpotent convex problems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {157--181},
     publisher = {mathdoc},
     volume = {291},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_291_a12/}
}
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L. V. Lokutsievskiy. On an optimal flow in a class of nilpotent convex problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 291 (2015), pp. 157-181. http://geodesic.mathdoc.fr/item/TM_2015_291_a12/