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This article is cited in 1 scientific paper (total in 1 paper)
On an optimal flow in a class of nilpotent convex problems
L. V. Lokutsievskiy Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Abstract:
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.
Received: December 15, 2014
Citation:
L. V. Lokutsievskiy, “On an optimal flow in a class of nilpotent convex problems”, Optimal control, Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 291, MAIK Nauka/Interperiodica, Moscow, 2015, 157–181; Proc. Steklov Inst. Math., 291 (2015), 146–169
Linking options:
https://www.mathnet.ru/eng/tm3669https://doi.org/10.1134/S0371968515040135 https://www.mathnet.ru/eng/tm/v291/p157
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