optimal control theory, theory of dynamical systems and convex analysis
Main publications:
M. I. Zelikin, L. V. Lokutsievskii, R. Hildebrand, “Typicality of Chaotic Fractal Behavior of Integral Vortices in Hamiltonian Systems with Discontinuous Right Hand Side”, Journal of Mathematical Sciences, 221:1 (2017), 1-136 , arXiv: 1506.02320
M. I. Zelikin, L. V. Lokutsievskiy, R. Hildebrand, “Geometry of neighborhoods of singular trajectories in problems with multidimensional control”, Proc. Steklov Inst. Math., 277 (2012), 67–83
L. V. Lokutsievskii, “The Hamiltonian property of the flow of singular trajectories”, Sb. Math., 205:3 (2014), 432–458
L. V. Lokutsievskiy, “On an optimal flow in a class of nilpotent convex problems”, Proc. Steklov Inst. Math., 291 (2015), 146–169
L. V. Lokutsievskii, “Homotopy classification of actions of finite groups on aspherical spaces”, J. Math. Sci., 177:2 (2011), 244-256
L. V. Lokutsievskiy, “Explicit Formulae for Geodesics in Left–Invariant Sub–Finsler Problems on Heisenberg Groups via Convex Trigonometry”, J. Dyn. Control Syst., 27 (2021), 661–681
2.
A. A. Ardentov, L. V. Lokutsievskiy, Yu. L. Sachkov, “Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry”, ESAIM: COCV, 27 (2021), 32 , 52 pp., arXiv: 2004.10194;
3.
M. I. Ronzhina, L. A. Manita, L. V. Lokutsievskiy, Optimal Control and Differential Games, Collected papers, Trudy MIAN, 315, Steklov Math. Inst., Moscow, 2021 (to appear)
4.
Lev Lokutsievskiy, Alexander Pechen, “Reachable sets for two-level open quantum systems driven by coherent and incoherent controls”, Journal of Physics A: Mathematical and Theoretical, 54:39 (2021), 395304 , 20 pp., arXiv: 2109.04384
5.
L. V. Lokutsievskiy, L. A. Manita, M. I. Ronzhina, “Solutions of a Hamiltonian system with two-dimensional control in the neighborhood of a singular extremal of the second order”, Uspekhi Mat. Nauk
2021
6.
A. I. Kushnir, L. V. Lokutsievskiy,, “When is a monotone function cyclically monotone?”, Theoretical Economics, 16:3 (2021), 853-879 https://onlinelibrary.wiley.com/doi/full/10.3982/TE4305 (cited: 1)
7.
Optimalnoe upravlenie i differentsialnye igry, Sbornik statei, Trudy MIAN, 315, ed. S. M. Aseev, L. V. Lokutsievskii, M. S. Nikolskii, MIAN, M., 2021
2020
8.
L. V. Lokutsievskiy, M. I. Zelikin, “The analytical solution of Newton’s aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary”, ESAIM: COCV, 26 (2020), 15 , 36 pp., arXiv: 1905.02028 (cited: 1) (cited: 1);
9.
A. A. Ardentov, L. V. Lokutsievskiy, Yu. L. Sachkov, “Explicit solutions for a series of optimization problems with 2-dimensional control via convex trigonometry”, Dokl. Math., 102 (2020), 427–432
2019
10.
L. V. Lokoutsievskiy, V. A. Myrikova, “Optimal Synthesis in a Model Problem with Two-Dimensional Control Lying in an Arbitrary Convex Set”, Math. Notes, 105:1 (2019), 36–55
11.
L. V. Lokutsievskiy, “Convex trigonometry with applications to sub-Finsler geometry”, Sb. Math., 210:8 (2019), 1179–1205 (cited: 5) (cited: 6)
12.
M. I. Zelikin, L. V. Lokutsievskiy, “Analytical solution of Newton's aerodynamic problem without the assumption of rotational symmetry”, Materialy Mezhdunarodnoi konferentsii "Ustoichivost, upravlenie, differentsialnye igry (SCDG2019)", posvyaschennoi 95-letiyu so dnya rozhdeniya akademika N.N. Krasovskogo (Ekaterinburg, 16–20 sentyabrya 2019 g.), IMM UrO RAN, 2019, 464 , arXiv: 1905.02028
13.
Lev V. Lokutsievskiy, “Convex trigonometry with applications to sub-Finsler geometry”, Materialy Mezhdunarodnoi konferentsii "Ustoichivost, upravlenie, differentsialnye igry (SCDG2019)", posvyaschennoi 95-letiyu so dnya rozhdeniya akademika N.N. Krasovskogo (Ekaterinburg, 16–20 sentyabrya 2019 g.), Institut matematiki i mekhaniki UrO RAN im. N.N. Krasovskogo, 2019, 435–436 , arXiv: 1807.08155
2018
14.
L. V. Lokutsievskiy, Yu. L. Sachkov, “Liouville integrability of sub-Riemannian problems on Carnot groups of step 4 or greater”, Sb. Math., 209:5 (2018), 672–713 (cited: 6) (cited: 8)
15.
L. V. Lokutsievskiy, M. I. Zelikin, “Hessian measures in the aerodynamic Newton problem”, J. Dyn. Control Syst., 24:3 (2018), 475–495 (cited: 2) (cited: 2)
16.
L. V. Lokutsievskiy, V. M. Tikhomirov, Kvant, 2018, no. 6, 11–17
17.
L. V. Lokutsievskiy, V. M. Tikhomirov, Kvant, 2018, no. 5, 2–8
2017
18.
A.V. Arutyunov, A.V. Greshnov, L.V. Lokutsievskii, K.V. Storozhuk, “Topological and geometrical properties of spaces with symmetric and nonsymmetric $f$-quasimetrics”, Topology Appl., 221 (2017), 178–194 (cited: 13) (cited: 16)
19.
M. I. Zelikin, L. V. Lokutsievskiy, S. V. Skopintcev, “On Optimal Harvesting of a Resource on a Circle”, Math. Notes, 102:4 (2017), 521–532 (cited: 3) (cited: 3)
20.
L. V. Lokutsievskiy, Yu. L. Sachkov, “Liouville nonintegrability of sub-Riemannian problems on free Carnot groups of step 4”, Dokl. Math., 95:3 (2017), 211–213 (cited: 2) (cited: 2)
21.
M. I. Zelikin, L. V. Lokutsievskii, R. Hildebrand, “Typicality of Chaotic Fractal Behavior of Integral Vortices in Hamiltonian Systems with Discontinuous Right Hand Side”, Journal of Mathematical Sciences, 221:1 (2017), 1-136 , arXiv: 1506.02320 (cited: 3)
2015
22.
L. V. Lokutsievskiy, “On an optimal flow in a class of nilpotent convex problems”, Proc. Steklov Inst. Math., 291 (2015), 146–169 (cited: 1)
23.
Lev Lokutsievskiy, Vincent Runge, “Optimal control by multipoles in the Hele-Shaw problem”, J. Math. Fluid Mech., 17:2 (2015), 261–277
2014
24.
L. V. Lokutsievskii, “Singular regimes in controlled systems with multidimensional control in a polyhedron.”, Izv. Math., 78:5 (2014), 1006–1027 (cited: 3) (cited: 1) (cited: 1) (cited: 2)
25.
L. V. Lokutsievskii, “Generic structure of the Lagrangian manifold in chattering problems”, Math. Notes, 95:6 (2014), 786–794
26.
L. V. Lokutsievskii, “The Hamiltonian property of the flow of singular trajectories”, Sb. Math., 205:3 (2014), 432–458 (cited: 2)
2013
27.
M. I. Zelikin, D. D. Kiselev, L. V. Lokutsievskii, “Optimal control and Galois theory”, Sb. Math., 204:11 (2013), 1624–1638 (cited: 3) (cited: 1) (cited: 1) (cited: 4)
28.
R. Hildebrand,L. V. Lokutsievskiy, M. I. Zelikin, “Generic Fractal Structure of Finite Parts of Trajectories of Piecewise Smooth Hamiltonian Systems”, Russ. J. Math. Phys., 20:1 (2013), 25–32 (cited: 3) (cited: 4)
29.
M. I. Zelikin, L. V. Lokutsievskii, R. Hildebrand, “Stochastic dynamics of lie algebras of Poisson brackets in neighborhoods of nonsmoothness points of Hamiltonians”, Dokl. Math., 87:3 (2013), 259–263 (cited: 1)
2012
30.
M. I. Zelikin, L. V. Lokutsievskiy, R. Hildebrand, “Geometry of neighborhoods of singular trajectories in problems with multidimensional control”, Proc. Steklov Inst. Math., 277 (2012), 67–83 (cited: 12) (cited: 4) (cited: 4) (cited: 6)
31.
L. V. Lokutsievskiy, “Fractal structure of hyperbolic Lipschitzian dynamical system”, Russ. J. Math. Phys., 19:1 (2012), 27–44 (cited: 3) (cited: 4)
2011
32.
L. V. Lokutsievskiy, “Optimal probabilistic search”, Sb. Math., 202:5 (2011), 697–719 (cited: 3) (cited: 1)
33.
L. V. Lokutsievskii, “Homotopy classification of actions of finite groups on aspherical spaces”, J. Math. Sci., 177:2 (2011), 244-256 (cited: 1) (cited: 1)
2009
34.
I. P. Kramarev, L. V. Lokutsievskiy, “Homotopy types of group lattices”, J. Math. Sci., 163:6 (2009), 694–708
35.
M. I. Zelikin, L. V. Lokutsievskii, R. A. Usachev, “Vortex singularities of optimal strategies at the beginning of motion in search problems on $n$-dimensional Riemannian manifolds”, J. Math. Sci., 160:2 (2009), 197–220
2007
36.
L. V. Lokutsievskii, “Vortex singularities of optimal strategies at the beginning of a motion in search problems on $n$-manifolds”, Dokl. Math., 76:3 (2007), 869–871 (cited: 1) (cited: 1) (cited: 1)
2008
37.
L. V. Lokutsievskii, “Accumulation of switchings in search problems”, J. Math. Sci., 151:6 (2008), 3497–3505
Singular extremals in the generalised Fuller problem M. I. Zelikin, D. D. Kiselev, L. V. Lokutsievskiy International Conference "Mathematical Theory of Optimal Control"
dedicated to the 90th birthday of Academician R. V. Gamkrelidze June 1, 2017 15:45
Flat (2,3,5,8) sub-Riemannian problem L. V. Lokutsievskii, Yu. L. Sachkov, E. F. Sachkova International Conference on Mathematical Control Theory and Mechanics July 4, 2015 17:20
33.
Фрактальная структура оптимального синтеза M. I. Zelikin, L. V. Lokutsievskii, R. Hildebrand All-Moscow regular scientific seminar "Control Theory and Optimization" December 2, 2014 11:30
Optimal Control and Differential Games, Collected papers, Trudy Mat. Inst. Steklova, 315, ed. S. M. Aseev, L. V. Lokutsievskiy, M. S. Nikol'skii, 2021 http://mi.mathnet.ru/book1869
2021
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