Persons: Zelikin Mikhail Il'ich

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Zelikin Mikhail Il'ich

Statistics Math-Net.Ru
Total publications:	32
Scientific articles:	26
Citations to the author:	30
Cited articles:	13
Citing authors:	8

Number of views:
This page:	960
Abstract pages:	3848
Full texts:	1243
References:	137

Scientific status:

Professor

Scientific degree:

Doctor of physico-mathematical sciences

Speciality:

01.01.02 (Differential equations)

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

M. I. Zelikin, Control Theory and Optimization I. Homogeneous Spaces and the Riccati Equation in the Calculus of Veriations, Springer-Verlag, Berlin, 2000
M. I. Zelikin, V. F. Borisov, Theory of Chattering Control with applications to Astronautics, Robotics, Economics, and Engineering, Birkhäuser, Boston, MA, 1994
M. I. Zelikin, Optimal control and variational calculus., URSS, Moscow, 2004
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
M. I. Zelikin, “Superconductivity of Plasma and Fireballs”, CMFD, 19, 2006, 45–69

List of publications on Google Scholar

List of publications on ZentralBlatt

Publications in Math-Net.Ru

1.	Accumulation of Switchings in Distributed Parameter Problems M. I. Zelikin, L. A. Manita CMFD, 2006, 19, 78–113
2.	Superconductivity of Plasma and Fireballs M. I. Zelikin CMFD, 2006, 19, 45–69
3.	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., 2006, 110, 134–154
4.	Optimal problems on Hölder function spaces M. I. Zelikin Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2006, 110, 109–133
5.	Geometry of operator cross ratio M. I. Zelikin Mat. Sb., 2006, 197:1, 39–54
6.	Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems M. I. Zelikin Mat. Sb., 2004, 195:6, 57–70
7.	Optimal chattering feedback control M. I. Zelikin, V. F. Borisov Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2002, 90, 5–189
8.	Chattering on optimal trajectories of Hölder problems M. I. Zelikin Mat. Sb., 2002, 193:5, 37–52
9.	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, 2002, 236, 174–196
10.	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, 2001, 233, 125–152
11.	Asymptotics of Optimal Synthesis for One Class of Extremal Problems M. I. Zelikin, L. F. Zelikina, R. Hildebrand Tr. Mat. Inst. Steklova, 2001, 233, 95–124
12.	Synthesis of Optimal Trajectories That Defines the Reeb Foliation M. I. Zelikin Tr. Mat. Inst. Steklova, 2001, 233, 89–94
13.	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, 1999, 54:3(327), 163–164
14.	Exact Constants in Kolmogorov-Type Inequalities M. I. Zelikin, L. F. Zelikina Tr. Mat. Inst. Steklova, 1999, 227, 137–145
15.	Optimal Synthesis Containing Successively Inserted Chattering Bundles M. I. Zelikin Tr. Mat. Inst. Steklova, 1999, 224, 152–164
16.	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., 1998, 189:10, 33–52
17.	Cartan–Siegel homogeneous domains as integral manifolds of the complex Riccati-type equation M. I. Zelikin Tr. Mat. Inst. Steklova, 1998, 220, 130–141
18.	On the connection generated by the problem of minimizing a multiple integral M. I. Zelikin Mat. Sb., 1997, 188:1, 59–72
19.	Irregularity of optimal control in regular extremal problems M. I. Zelikin Fundam. Prikl. Mat., 1995, 1:2, 399–408
20.	On the theory of the matrix Riccati equation. II M. I. Zelikin Mat. Sb., 1992, 183:10, 87–108
21.	On the theory of the matrix Riccati equation M. I. Zelikin Mat. Sb., 1991, 182:7, 970–984
22.	Regimes with frequented switches in the problems of optimal control M. I. Zelikin, V. F. Borisov Trudy Mat. Inst. Steklov., 1991, 197, 85–166
23.	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, 1990, 47:1, 62–73
24.	Group symmetry in degenerate extremal problems M. I. Zelikin Uspekhi Mat. Nauk, 1988, 43:2(260), 139–140
25.	Synthesis of optimal trajectories on representation spaces of Lie groups M. I. Zelikin Mat. Sb. (N.S.), 1987, 132(174):4, 541–555
26.	Determined differential games M. I. Zelikin, N. T. Tynyanskii Uspekhi Mat. Nauk, 1965, 20:4(124), 151–157

27.	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, 2006, 61:1(367), 187–190
28.	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., 2005, 5:1, 295
29.	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, 2001, 56:6(342), 167–170
30.	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, 1998, 53:5(323), 213–220
31.	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, 1986, 41:4(250), 143–144
32.	Vladimir Mikhailovich Alekseev (obituary) D. V. Anosov, V. I. Arnol'd, M. I. Zelikin, A. N. Kolmogorov, O. V. Lokutsievskii, Yu. S. Osipov, Ya. G. Sinai, V. M. Tikhomirov, M. V. Jakobson Uspekhi Mat. Nauk, 1981, 36:4(220), 177–182

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