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This article is cited in 2 scientific papers (total in 2 papers)
CONTROL PROCESSES
Periodic time-optimal controls on two-step free-nilpotent Lie groups
Yu. L. Sachkovab a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation
b Ailamazyan Program Systems Institute of Russian Academy of Sciences, Pereslavl-Zalessky, Yaroslavl Region, Russian Federation
Abstract:
For two-step free nilpotent Lie algebras, we describe symplectic foliations and Casimir functions. A left-invariant time-optimal problem is considered in which the set of admissible controls is given by a strictly convex compact set in the first layer of the Lie algebra that contains the origin in its interior. We describe integrals for the vertical subsystem of the Hamiltonian system of the Pontryagin maximum principle. The properties of solutions to this system for low ranks of the Poisson bivector are described.
Keywords:
symplectic foliations, Casimir functions, time-optimal control problem, Pontryagin maximum principle, periodic controls.
Citation:
Yu. L. Sachkov, “Periodic time-optimal controls on two-step free-nilpotent Lie groups”, Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020), 108–111; Dokl. Math., 101:3 (2020), 262–264
Linking options:
https://www.mathnet.ru/eng/danma84 https://www.mathnet.ru/eng/danma/v492/p108
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Abstract page: | 115 | Full-text PDF : | 33 | References: | 19 |
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