Abstract
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.
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References
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)].
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)].
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Russian Text © L. V. Lokutsievskiy, V. A. Myrikova, 2019, published in Matematicheskie Zametki, 2019, Vol. 105, No. 1, pp. 42–64.
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Lokutsievskiy, L.V., Myrikova, V.A. Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set. Math Notes 105, 36–55 (2019). https://doi.org/10.1134/S000143461901005X
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DOI: https://doi.org/10.1134/S000143461901005X