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Subbotina, Nina Nikolaevna
Corresponding member of RAS
Professor
Doctor of physico-mathematical sciences (1976)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 2.08.1946
E-mail:
Website: http://www.uran.ru/members/corr/subbotina
Keywords: Hamilton–Jacobi equations, minimax and/or viscosity solutions, positional differential games, differential inclusions, invariance and/or viability theory.
   
Main publications:
  • Subbotina N. N., Subbotin A. I., Tret'jakov V. E. Stochastic and deterministic // Control. Differential Inequalities. Lect. Notes Control and Inform. Sciences, V. 81: Stochastic Optimization, Arkin V. I., Shiryaev A. N., Wets R. Eds., Berlin–New York: Springer-Verlag, 1986, 728–736.
  • Subbotina N. N. Singular Approximations of Minimax and Viscosity Solutions to Hamilton–Jacobi Equations // Proc. Steklov Institute of Math. Suppl. 1., 2000, Proc. Institute Math. Mech., Ural Branch, Russian Acad. Sci., Control in Dynamic Systems, MAIK "Nauka/Interperiodica" Publishing, S210–S227.

https://www.mathnet.ru/eng/person17603
https://ru.wikipedia.org/wiki/Subbotina,_Nina_Nikolaevna_(matematik)
List of publications on Google Scholar
https://zbmath.org/authors/ai:subbotina.nina-n
https://mathscinet.ams.org/mathscinet/MRAuthorID/190763
https://elibrary.ru/author_items.asp?authorid=164220
https://orcid.org/0000-0002-2056-7499
https://www.scopus.com/authid/detail.url?authorId=7004386095
https://www.researchgate.net/profile/Nina-Subbotina-2

Publications in Math-Net.Ru Citations
2024
1. N. N. Subbotina, A. S. Rodin, “Generalized Hopf formula for the value function in the positional differential game “Boy and Crocodile””, Trudy Inst. Mat. i Mekh. UrO RAN, 30:3 (2024),  229–240  mathnet  elib
2. N. N. Subbotina, E. A. Krupennikov, “On a control reconstruction problem with nonconvex constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 30:2 (2024),  188–202  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 325, suppl. 1 (2024), S179–S193  scopus
2021
3. N. N. Subbotina, E. A. Krupennikov, “Weak* Approximations to the Solution of a Dynamic Reconstruction Problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 27:2 (2021),  208–220  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 317, suppl. 1 (2022), S142–S152  isi  scopus 4
4. N. N. Subbotina, E. A. Krupennikov, “Weak* Solution to a Dynamic Reconstruction Problem”, Trudy Mat. Inst. Steklova, 315 (2021),  247–260  mathnet; Proc. Steklov Inst. Math., 315 (2021), 233–246  isi  scopus 5
2020
5. Nina N. Subbotina, “On control reconstructions to management problems”, Contributions to Game Theory and Management, 13 (2020),  402–414  mathnet
6. N. G. Novoselova, N. N. Subbotina, “Construction of the viability set in a problem of chemotherapy of a malignant tumor growing according to the Gompertz law”, Trudy Inst. Mat. i Mekh. UrO RAN, 26:1 (2020),  173–181  mathnet  elib
2019
7. N. N. Subbotina, N. G. Novoselova, “On Applications of the Hamilton–Jacobi Equations and Optimal Control Theory to Problems of Chemotherapy of Malignant Tumors”, Trudy Mat. Inst. Steklova, 304 (2019),  273–284  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 304 (2019), 257–267  isi  scopus 1
2017
8. N. N. Subbotina, N. G. Novoselova, “Optimal result in a control problem with piecewise monotone dynamics”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:4 (2017),  265–280  mathnet  elib 3
2016
9. N. N. Subbotina, E. A. Krupennikov, “The method of characteristics in an identification problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:2 (2016),  255–266  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 205–216  isi  scopus 11
2015
10. N. N. Subbotina, L. G. Shagalova, “The construction of a continuous generalized solution for the Hamilton–Jacobi equations with state constraints”, Izv. IMI UdGU, 2015, no. 2(46),  193–201  mathnet  elib
11. N. N. Subbotina, L. G. Shagalova, “On the continuous extension of a generalized solution of the Hamilton-Jacobi equation by characteristics that form a central field of extremals”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:2 (2015),  220–235  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 183–198  isi  scopus 5
12. N. N. Subbotina, T. B. Tokmantsev, E. A. Krupennikov, “On the solution of inverse problems of dynamics of linearly controlled systems by the negative discrepancy method”, Trudy Mat. Inst. Steklova, 291 (2015),  266–275  mathnet  elib; Proc. Steklov Inst. Math., 291 (2015), 253–262  isi  scopus 14
2014
13. N. N. Subbotina, L. G. Shagalova, “Construction of a continuous minimax/viscosity solution of the Hamilton–Jacobi–Bellman equation with nonextendable characteristics”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:4 (2014),  247–257  mathnet  mathscinet  elib 2
14. N. N. Subbotina, T. B. Tokmantsev, “A study of the stability of solutions to inverse problems of dynamics of control systems under perturbations of initial data”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:3 (2014),  218–233  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 173–189  isi  scopus 5
2012
15. N. N. Subbotina, L. G. Shagalova, “On constructions of the generalized solution of the Hamilton–Jacobi equation in bounded domains”, Izv. IMI UdGU, 2012, no. 1(39),  126–127  mathnet
16. N. N. Subbotina, L. G. Shagalova, “Construction of a generalized solution to an equation that preserves the Bellman type in a given domain of the state space”, Trudy Mat. Inst. Steklova, 277 (2012),  243–256  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 277 (2012), 234–247  isi  elib  scopus 6
2011
17. N. N. Subbotina, E. A. Kolpakova, “Method of characteristics for optimal control problems and conservation laws”, CMFD, 42 (2011),  204–210  mathnet  mathscinet; Journal of Mathematical Sciences, 199:5 (2014), 588–595  scopus 1
18. N. N. Subbotina, L. G. Shagalova, “On a solution to the Cauchy problem for the Hamilton–Jacobi equation with state constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 17:2 (2011),  191–208  mathnet  elib 12
2010
19. Nina N. Subbotina, Timofei B. Tokmantsev, “The Method of Characteristics in Macroeconomic Modeling”, Contributions to Game Theory and Management, 3 (2010),  399–408  mathnet
20. N. N. Subbotina, T. B. Tokmantsev, “Classical characteristics of the Bellman equation in constructions of grid optimal synthesis”, Trudy Mat. Inst. Steklova, 271 (2010),  259–277  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 271 (2010), 246–264  isi  elib  scopus 5
2009
21. N. N. Subbotina, T. B. Tokmantsev, “Estimating error of the optimal grid design in the problems of nonlinear optimal control of prescribed duration”, Avtomat. i Telemekh., 2009, no. 9,  141–156  mathnet  mathscinet  zmath; Autom. Remote Control, 70:9 (2009), 1565–1578  isi  scopus 2
22. N. N. Subbotina, E. A. Kolpakova, “On the structure of locally Lipschitz minimax solutions of the Hamilton–Jacobi–Bellman equation in terms of classical characteristics”, Trudy Inst. Mat. i Mekh. UrO RAN, 15:3 (2009),  202–218  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S222–S239  isi  scopus 8
2008
23. N. N. Subbotina, T. B. Tokmantsev, “Optimal Synthesis in a Control Problem with Lipschitz Input Data”, Trudy Mat. Inst. Steklova, 262 (2008),  240–252  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 262 (2008), 231–243  isi  elib  scopus 1
24. N. N. Subbotina, L. G. Shagalova, “On the structure of the solution of the Hamilton-Jacobi equation with piecewise linear input data”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, no. 2,  144–147  mathnet
2007
25. E. A. Kolpakova, N. N. Subbotina, “Defining the asymptotics for one class of singularly perturbed problems of vibrational mechanics”, Avtomat. i Telemekh., 2007, no. 11,  150–163  mathnet  mathscinet  zmath; Autom. Remote Control, 68:11 (2007), 2029–2041  scopus 2
2006
26. N. N. Subbotina, T. B. Tokmantsev, “The method of generalized characteristics in an optimal control problem with Lipschitz inputs”, Izv. IMI UdGU, 2006, no. 3(37),  141–142  mathnet
27. N. N. Subbotina, T. B. Tokmantsev, “A numerical method for the minimax solution of the Bellman equation in the Cauchy problem with additional restrictions”, Trudy Inst. Mat. i Mekh. UrO RAN, 12:1 (2006),  208–215  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 253, suppl. 1 (2006), S221–S228  scopus 4
2004
28. N. N. Subbotina, “Adjoint variables to optimal control problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 10:2 (2004),  131–141  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2004no. , suppl. 2, S142–S153
2000
29. N. N. Subbotina, “Singular approximations of minimax and viscosity solutions to Hamilton–Jacobi equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 6:1 (2000),  190–208  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2000no. , suppl. 1, S210–S227 6
1993
30. A. I. Subbotin, N. N. Subbotina, “Piecewise-smooth solutions of first-order partial differential equations”, Dokl. Akad. Nauk, 333:6 (1993),  705–707  mathnet  mathscinet  zmath; Dokl. Math., 48:3 (1994), 650–654 1
1992
31. N. N. Subbotina, “Unified optimality conditions in control problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 1 (1992),  147–159  mathnet  mathscinet  zmath  elib 3
1991
32. N. N. Subbotina, “The method of Cauchy characteristics and generalized solutions of the Hamilton–Jacobi–Bellman equation”, Dokl. Akad. Nauk SSSR, 320:3 (1991),  556–561  mathnet  mathscinet  zmath; Dokl. Math., 44:2 (1992), 501–506 2
1983
33. N. N. Subbotina, “Universal optimal strategies in positional differential games”, Differ. Uravn., 19:11 (1983),  1890–1896  mathnet  mathscinet 9
1982
34. A. I. Subbotin, N. N. Subbotina, “The optimum result function in a control problem”, Dokl. Akad. Nauk SSSR, 266:2 (1982),  294–299  mathnet  mathscinet  zmath 7
1978
35. A. I. Subbotin, N. N. Subbotina, “Necessary and sufficient conditions for a piecewise smooth value of a differential game”, Dokl. Akad. Nauk SSSR, 243:4 (1978),  862–865  mathnet  mathscinet  zmath 8
2014
36. V. I. Berdyshev, V. V. Vasin, S. V. Matveev, A. A. Makhnev, Yu. N. Subbotin, N. N. Subbotina, V. N. Ushakov, M. Yu. Khachai, A. G. Chentsov, “Ivan Ivanovich Eremin”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:2 (2014),  5–12  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 1–8  isi
2010
37. N. N. Subbotina, A. I. Korotkii, “Actual problems of stability and control theory (APSCT'2009)”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:5 (2010),  3–7  mathnet  elib

Presentations in Math-Net.Ru
1. О решении обратных задач теории управления с помощью гамильтоновых конструкций
E. A. Krupennikov, N. N. Subbotina

November 8, 2022 15:25
2. Non-convex and convex variational approaches to solving a control reconstruction problem
N. N. Subbotina, E. A. Krupennikov
International Conference “Differential Equations and Optimal Control” dedicated to the centenary of the birth of Academician Evgenii Frolovich Mishchenko
June 9, 2022 12:30   
3. Adjoint variables in dynamic reconstruction problems
N. N. Subbotina, T. B. Tokmantsev
International conference "Systems Analysis: Modeling and Control" in memory of Academician A. V. Kryazhimskiy
June 1, 2018 14:30
4. Hamiltonian systems in solutions of boundary problems with state constraints for Hamilton–Jacobi–Bellman equations
N. N. Subbotina
International Conference "Mathematical Theory of Optimal Control" dedicated to the 90th birthday of Academician R. V. Gamkrelidze
June 1, 2017 11:50   
5. The method of characteristics to identification problems
N. N. Subbotina
International conference "Dynamical Systems: Inverse Problems, Stability and Control Processes" dedicated to the 80th birthday of Yu. S. Osipov
September 22, 2016 17:20   
6. Optimal synthesis in dynamic problems
N. N. Subbotina
Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin
September 24, 2013 13:10   

Organisations
 
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