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, A. V. Podobryaev, “Existence theorem for sub-Lorentzian problems”, J. Dyn. Control Syst., 30 (2024), 10 , 12 pp. ;
2.
L. V. Lokutsievskiy, A. N. Pechen, M. I. Zelikin, “Time-optimal state transfer for an open qubit”, J. Phys. A, 57:27 (2024), 275302 , 23 pp., arXiv: 2401.10099;
3.
A. V. Dymov, L. V. Lokutsievskiy, A. V. Sarychev, “Strict Lyapunov functions and energy decay in Hamiltonian chains with degenerate damping”, Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, Steklov Math. Inst., Moscow, 2024 (to appear)
2023
4.
Lev V. Lokutsievskiy, Alexander I. Ovseevich, “Asymptotic Control Theory for a Closed String. II”, Proc. Steklov Inst. Math., 321 (2023), 179–199 , arXiv: 2202.09087
5.
Lev Lokutsievskiy, Mikhail Zelikin, “Derivatives of sub-Riemannian geodesics are $L_p$-Hölder continuous”, ESAIM: COCV, 29 (2023), 70 , 30 pp., arXiv: 2203.04956;
Optimalnoe upravlenie i dinamicheskie sistemy, Sbornik statei. K 95-letiyu akademika Revaza Valerianovicha Gamkrelidze, Trudy MIAN, 321, ed. A. A. Agrachev, L. V. Lokutsievskii, A. V. Sarychev, Yu. L. Sachkov, MIAN, M., 2023 , 292 pp.
2022
7.
Lev Lokutsievskiy, Gerd Wachsmuth, Mikhail Zelikin, “Non-optimality of conical parts for Newton’s problem of minimal resistance in the class of convex bodies and the limiting case of infinite height”, Calc. Var. Partial Differential Equations, 61:1 (2022), 31 , 18 pp. ;
2021
8.
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 , arXiv: 2005.08941
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;
M. I. Ronzhina, L. A. Manita, L. V. Lokutsievskiy, “Neighborhood of the Second-Order Singular Regime in Problems with Control in a Disk”, Proc. Steklov Inst. Math., 315 (2021), 209–222
11.
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
M. I. Ronzhina, L. A. Manita, L. V. Lokutsievskiy, “Solutions of a Hamiltonian system with two-dimensional control in a neighbourhood of a singular second-order extremal”, Russian Math. Surveys, 76:5 (2021), 936–938
13.
Alexey I. Kushnir, Lev V. Lokutsievskiy, “When is a monotone function cyclically monotone?”, Theor. Econ., 16:3 (2021), 853–879;
Optimalnoe upravlenie i differentsialnye igry, Sbornik statei, Trudy MIAN, 315, ed. S. M. Aseev, L. V. Lokutsievskii, M. S. Nikolskii, MIAN, M., 2021 , 304 pp.
2020
15.
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;
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
17.
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
18.
L. V. Lokutsievskiy, “Convex trigonometry with applications to sub-Finsler geometry”, Sb. Math., 210:8 (2019), 1179–1205 , arXiv: 1807.08155
19.
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
20.
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
21.
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
22.
L. V. Lokutsievskiy, M. I. Zelikin, “Hessian measures in the aerodynamic Newton problem”, J. Dyn. Control Syst., 24:3 (2018), 475–495
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
27.
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
28.
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
2015
29.
L. V. Lokutsievskiy, “On an optimal flow in a class of nilpotent convex problems”, Proc. Steklov Inst. Math., 291 (2015), 146–169
30.
Lev Lokutsievskiy, Vincent Runge, “Optimal control by multipoles in the Hele-Shaw problem”, J. Math. Fluid Mech., 17:2 (2015), 261–277
2014
31.
L. V. Lokutsievskii, “Singular regimes in controlled systems with multidimensional control in a polyhedron.”, Izv. Math., 78:5 (2014), 1006–1027
32.
L. V. Lokutsievskii, “Generic structure of the Lagrangian manifold in chattering problems”, Math. Notes, 95:6 (2014), 786–794
33.
L. V. Lokutsievskii, “The Hamiltonian property of the flow of singular trajectories”, Sb. Math., 205:3 (2014), 432–458
2013
34.
M. I. Zelikin, D. D. Kiselev, L. V. Lokutsievskii, “Optimal control and Galois theory”, Sb. Math., 204:11 (2013), 1624–1638
35.
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
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
2012
37.
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
38.
L. V. Lokutsievskiy, “Fractal structure of hyperbolic Lipschitzian dynamical system”, Russ. J. Math. Phys., 19:1 (2012), 27–44
I. P. Kramarev, L. V. Lokutsievskiy, “Homotopy types of group lattices”, J. Math. Sci., 163:6 (2009), 694–708
42.
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
43.
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
2008
44.
L. V. Lokutsievskii, “Accumulation of switchings in search problems”, J. Math. Sci., 151:6 (2008), 3497–3505
Presentations in Math-Net.Ru
1.
Отдел дифференциальных уравнений L. V. Lokutsievskiy Conference MIAN-90, dedicated to the 90th anniversary of Steklov Mathematical Institute May 15, 2024 11:30
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
50.
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 Dynamical Systems, Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze, Trudy Mat. Inst. Steklova, 321, ed. A. A. Agrachev, L. V. Lokutsievskiy, A. V. Sarychev, Yu. L. Sachkov, 2023, 292 с. http://mi.mathnet.ru/book1935
Optimal Control and Differential Games, Collected papers, Trudy Mat. Inst. Steklova, 315, ed. S. M. Aseev, L. V. Lokutsievskiy, M. S. Nikol'skii, 2021, 304 с. http://mi.mathnet.ru/book1869
2024
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