Mathematical Notes

, Volume 105, Issue 1–2, pp 36–55 | Cite as

Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set

  • L. V. LokutsievskiyEmail author
  • V. A. MyrikovaEmail author


We consider a model nilpotent convex problem with two-dimensional control from an arbitrary convex set Ω. For the case in which Ω is a polygon, the problem is solved explicitly. For the case of an arbitrary set Ω, we completely describe the asymptotics of optimal trajectories and the geometric properties of the optimal synthesis.


optimal synthesis two-dimensional control nilpotent convex problem 


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  1. 1.
    L. V. Lokutsievskiy, “Singular regimes in controlled systems with multidimensional control in a polyhedron,” Izv. Ross. Akad. Nauk Ser. Mat. 78 (5), 167–190 (2014) [Izv. Math. 78 (5), 1006–1027 (2014)].MathSciNetCrossRefGoogle Scholar
  2. 2.
    L. V. Lokutsievskiy, “On an optimal flow in a class of nilpotent convex problems,” in Trudy Mat. Inst. Steklova, Vol. 291: Optimal Control (MAIK Nauka/Interperiodica, Moscow, 2015), pp. 157–181 [Proc. Steklov Inst. Math. 291, 146–169 (2015)].MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia
  2. 2.OOO “Execution RDC,”MoscowRussia

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