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, 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;
2.
L. V. Lokutsievskiy, “Explicit Formulae for Geodesics in Left–Invariant Sub–Finsler Problems on Heisenberg Groups via Convex Trigonometry”, J. Dyn. Control Syst., 2020, 1–21 (Published online) ; (Published online)
3.
A. A. Ardentov, L. V. Lokutsievskii, Yu. L. Sachkov, “Reshenie serii zadach optimalnogo upravleniya s 2-mernym upravleniem na osnove vypukloi trigonometrii”, Doklady Rossiiskoi akademii nauk. Matematika, informatika, protsessy upravleniya, 494:1 (2020), 86-92
2019
4.
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
5.
L. V. Lokutsievskiy, “Convex trigonometry with applications to sub-Finsler geometry”, Sb. Math., 210:8 (2019), 1179–1205 (cited: 2) (cited: 3)
6.
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
7.
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
8.
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: 4) (cited: 5)
9.
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)
2017
10.
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)
11.
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)
12.
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)
13.
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: 2)
2015
14.
L. V. Lokutsievskiy, “On an optimal flow in a class of nilpotent convex problems”, Proc. Steklov Inst. Math., 291 (2015), 146–169 (cited: 1)
15.
Lev Lokutsievskiy, Vincent Runge, “Optimal control by multipoles in the Hele-Shaw problem”, J. Math. Fluid Mech., 17:2 (2015), 261–277
2014
16.
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)
17.
L. V. Lokutsievskii, “Generic structure of the Lagrangian manifold in chattering problems”, Math. Notes, 95:6 (2014), 786–794
18.
L. V. Lokutsievskii, “The Hamiltonian property of the flow of singular trajectories”, Sb. Math., 205:3 (2014), 432–458 (cited: 2)
2013
19.
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)
20.
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)
21.
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
22.
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: 11) (cited: 4) (cited: 4) (cited: 5)
23.
L. V. Lokutsievskiy, “Fractal structure of hyperbolic Lipschitzian dynamical system”, Russ. J. Math. Phys., 19:1 (2012), 27–44 (cited: 3) (cited: 4)
2011
24.
L. V. Lokutsievskiy, “Optimal probabilistic search”, Sb. Math., 202:5 (2011), 697–719 (cited: 3) (cited: 1)
25.
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
26.
I. P. Kramarev, L. V. Lokutsievskiy, “Homotopy types of group lattices”, J. Math. Sci., 163:6 (2009), 694–708
27.
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
28.
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
29.
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
31.
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
2020
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