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Zelikin Mikhail Il'ich

Statistics Math-Net.Ru
Total publications: 39
Scientific articles: 32
Citations to the author: 61
Cited articles: 20
Presentations: 9

Number of views:
This page:2852
Abstract pages:11492
Full texts:3318
References:351
Zelikin Mikhail Il'ich
Corresponding member of RAS
Professor
Doctor of physico-mathematical sciences
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 11.02.1936
E-mail:
Keywords: Optimal Control Theory, Chattering control, multiple integrals, cross ratio, Riccati equation, phase constraints, Pontryagin's maximum principle, Lagrangian manifolds, blow up.
UDC: 512.542, 517.551, 517.958, 517.977, 517.977.5, 519.9, 517
MSC: 37K10, 37K20

Subject

Optimal control theory, differential equations, differential games.

   
Main publications:
  1. M. I. Zelikin, Control Theory and Optimization I. Homogeneous Spaces and the Riccati Equation in the Calculus of Veriations, Springer-Verlag, Berlin, 2000  mathscinet
  2. M. I. Zelikin, V. F. Borisov, Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering, Birkhäuser, Boston, MA, 1994  mathscinet  zmath
  3. M. I. Zelikin, Optimal control and variational calculus., URSS, Moscow, 2004
  4. M. I. Zelikin, “Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems”, Mat. Sb., 195:6 (2004), 57–70  mathnet  mathscinet  zmath
  5. M. I. Zelikin, “Superconductivity of Plasma and Fireballs”, CMFD, 19, 2006, 45–69  mathnet

http://www.mathnet.ru/eng/person8494
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:zelikin.michail-i|zelikin.mikhail-i
http://www.ams.org/mathscinet/search/author.html?return=viewitems&mrauthid=207861

Publications in Math-Net.Ru
1. Optimal control and Galois theory
M. I. Zelikin, D. D. Kiselev, L. V. Lokutsievskii
Mat. Sb., 204:11 (2013),  83–98
2. Chattering regimes and Lagrangian manifolds in problems with phase constraints
V. F. Borisov, V. V. Gael, M. I. Zelikin
Izv. RAN. Ser. Mat., 76:1 (2012),  3–42
3. Theory and applications of the problem of Euler elastica
M. I. Zelikin
Uspekhi Mat. Nauk, 67:2(404) (2012),  93–108
4. Geometry of neighborhoods of singular trajectories in problems with multidimensional control
M. I. Zelikin, L. V. Lokutsievskiy, R. Hildebrand
Tr. Mat. Inst. Steklova, 277 (2012),  74–90
5. Theory of fields of extremals for multiple integrals
M. I. Zelikin
Uspekhi Mat. Nauk, 66:4(400) (2011),  103–136
6. Optimal synthesis in an infinite-dimensional space
V. F. Borisov, M. I. Zelikin, L. A. Manita
Tr. Mat. Inst. Steklova, 271 (2010),  40–58
7. Accumulation of Switchings in Distributed Parameter Problems
M. I. Zelikin, L. A. Manita
CMFD, 19 (2006),  78–113
8. Superconductivity of Plasma and Fireballs
M. I. Zelikin
CMFD, 19 (2006),  45–69
9. The Bellman function and optimal synthesis in control problems with nonsmooth constraints
M. I. Zelikin, N. B. Melnikov
Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 110 (2006),  134–154
10. Optimal problems on Hölder function spaces
M. I. Zelikin
Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 110 (2006),  109–133
11. Geometry of operator cross ratio
M. I. Zelikin
Mat. Sb., 197:1 (2006),  39–54
12. Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems
M. I. Zelikin
Mat. Sb., 195:6 (2004),  57–70
13. Optimal chattering feedback control
M. I. Zelikin, V. F. Borisov
Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 90 (2002),  5–189
14. Chattering on optimal trajectories of Hölder problems
M. I. Zelikin
Mat. Sb., 193:5 (2002),  37–52
15. The Structure of Optimal Synthesis in the Vicinity of Singular Manifolds for Problems Affine with Respect to Control
M. I. Zelikin
Tr. Mat. Inst. Steklova, 236 (2002),  174–196
16. The Topological Structure of the Phase Portrait of a Typical Fiber of Optimal Synthesis for Chattering Problems
M. I. Zelikin, N. B. Melnikov, R. Hildebrand
Tr. Mat. Inst. Steklova, 233 (2001),  125–152
17. Asymptotics of Optimal Synthesis for One Class of Extremal Problems
M. I. Zelikin, L. F. Zelikina, R. Hildebrand
Tr. Mat. Inst. Steklova, 233 (2001),  95–124
18. Synthesis of Optimal Trajectories That Defines the Reeb Foliation
M. I. Zelikin
Tr. Mat. Inst. Steklova, 233 (2001),  89–94
19. The asymptotics of the deviation of a functional from its optimal value when chattering is replaced by a suboptimal regime
M. I. Zelikin
Uspekhi Mat. Nauk, 54:3(327) (1999),  163–164
20. Exact Constants in Kolmogorov-Type Inequalities
M. I. Zelikin, L. F. Zelikina
Tr. Mat. Inst. Steklova, 227 (1999),  137–145
21. Optimal Synthesis Containing Successively Inserted Chattering Bundles
M. I. Zelikin
Tr. Mat. Inst. Steklova, 224 (1999),  152–164
22. The structure of optimal synthesis in a neighbourhood of singular manifolds for problems that are affine in control
M. I. Zelikin, L. F. Zelikina
Mat. Sb., 189:10 (1998),  33–52
23. Cartan–Siegel homogeneous domains as integral manifolds of the complex Riccati-type equation
M. I. Zelikin
Tr. Mat. Inst. Steklova, 220 (1998),  130–141
24. On the connection generated by the problem of minimizing a multiple integral
M. I. Zelikin
Mat. Sb., 188:1 (1997),  59–72
25. Irregularity of optimal control in regular extremal problems
M. I. Zelikin
Fundam. Prikl. Mat., 1:2 (1995),  399–408
26. On the theory of the matrix Riccati equation. II
M. I. Zelikin
Mat. Sb., 183:10 (1992),  87–108
27. On the theory of the matrix Riccati equation
M. I. Zelikin
Mat. Sb., 182:7 (1991),  970–984
28. Regimes with frequented switches in the problems of optimal control
M. I. Zelikin, V. F. Borisov
Trudy Mat. Inst. Steklov., 197 (1991),  85–166
29. Synthesis in problems of optimal control containing trajectories with participating switchings and singular trajectories of the second order
M. I. Zelikin, V. F. Borisov
Mat. Zametki, 47:1 (1990),  62–73
30. Group symmetry in degenerate extremal problems
M. I. Zelikin
Uspekhi Mat. Nauk, 43:2(260) (1988),  139–140
31. Synthesis of optimal trajectories on representation spaces of Lie groups
M. I. Zelikin
Mat. Sb. (N.S.), 132(174):4 (1987),  541–555
32. Determined differential games
M. I. Zelikin, N. T. Tynyanskii
Uspekhi Mat. Nauk, 20:4(124) (1965),  151–157

33. In memory of Evgenii Frolovich Mishchenko
Yu. S. Osipov, V. V. Kozlov, L. D. Faddeev, D. V. Anosov, V. S. Vladimirov, R. V. Gamkrelidze, A. A. Gonchar, N. N. Krasovskii, A. V. Kryazhimskii, A. B. Kurzhanskii, S. P. Novikov, S. M. Aseev, A. B. Zhizhchenko, D. V. Treschev, A. A. Agrachev, E. A. Volkov, N. L. Grigorenko, A. A. Davydov, M. I. Zelikin, A. Yu. Kolesov, A. A. Mal'tsev, M. S. Nikol'skii, N. Kh. Rozov, A. G. Sergeev, K. O. Besov, S. P. Konovalov
Tr. Mat. Inst. Steklova, 271 (2010),  7–8
34. Vladimir Mikhailovich Tikhomirov (on his 70th birthday)
V. I. Arnol'd, L. R. Volevich, A. A. Gonchar, S. S. Demidov, M. I. Zelikin, Yu. S. Ilyashenko, G. G. Magaril-Il'yaev, A. V. Mikhalev, S. P. Novikov, I. V. Yaschenko
Uspekhi Mat. Nauk, 61:1(367) (2006),  187–190
35. Vladimir M. Tikhomirov
V. I. Arnol'd, A. S. Demidov, Yu. S. Ilyashenko, G. G. Magaril-Il'yaev, E. F. Mishchenko, K. Yu. Osipenko, A. B. Sossinski, M. A. Tsfasman, V. A. Uspenskii, M. N. Vyalyi, I. V. Yaschenko, M. I. Zelikin
Mosc. Math. J., 5:1 (2005),  295
36. Aleksandr Sergeevich Mishchenko (on his 60th birthday)
A. A. Bolibrukh, A. A. Irmatov, M. I. Zelikin, O. B. Lupanov, V. M. Maynulov, E. F. Mishchenko, M. M. Postnikov, Yu. P. Solov'ev, E. V. Troitskii
Uspekhi Mat. Nauk, 56:6(342) (2001),  167–170
37. Stanislav Nikolaevich Kruzhkov (obituary)
N. S. Bakhvalov, M. I. Zelikin, A. S. Kalashnikov, V. L. Kamynin, O. A. Oleinik, E. Yu. Panov, N. S. Petrosyan, V. M. Tikhomirov, A. V. Faminskii, V. N. Chubarikov
Uspekhi Mat. Nauk, 53:5(323) (1998),  213–220
38. Nicolai Terent'evich Tynyanskii (obituary)
A. G. Vitushkin, M. I. Zelikin, N. N. Krasovskii, S. P. Novikov, Yu. S. Osipov, K. A. Sitnikov
Uspekhi Mat. Nauk, 41:4(250) (1986),  143–144
39. Vladimir Mikhailovich Alekseev (obituary)
D. V. Anosov, V. I. Arnol'd, M. I. Zelikin, Yu. S. Osipov, A. N. Kolmogorov, O. V. Lokutsievskii, Ya. G. Sinai, V. M. Tikhomirov, M. V. Jakobson
Uspekhi Mat. Nauk, 36:4(220) (1981),  177–182

Presentations in Math-Net.Ru
1. Chaos in optimal synthesis in problems with multidimensional control (part I)
The International Conference "Geometric Control Theory and Analysis on Metric Structures"
August 4, 2014 15:00
2. Singular orbits in hamiltonian systems with discontinous right term
Differential geometry and applications
March 24, 2014 16:45
3. Chaotic dynamics of optimal trajectories in problems with multidimensional control
Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin
September 24, 2013 11:10   
4. Stochastic dynamics of Lie algebras of Poisson brackets in a neighbourhood of the points where the Hamiltonian is not smooth
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
April 3, 2013 16:45
5. Стохастическая динамика алгебр Ли скобок Пуассона в окрестности точек негладкости гамильтониана
Meetings of the Moscow Mathematical Society
February 12, 2013 18:30
6. Euler's elastics and elastic shells
Differential geometry and applications
November 26, 2012 16:45
7. Fields of extremals for multiple integrals
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
March 23, 2011 16:45
8. Теория поля экстремалей для функционалов типа кратных интегралов
Meetings of the Moscow Mathematical Society
March 23, 2010
9. Фазовый портрет с накоплением переключений в бесконечномерном пространстве
Seminar of the Department of Differential Equations, Steklov Mathematical Institute
April 2, 2008 12:00

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