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Uspenskii, Aleksandr Aleksandrovich
Statistics Math-Net.Ru
Total publications: 47
Scientific articles: 47
Presentations: 1

Number of views:
This page:4907
Abstract pages:14745
Full texts:4493
References:2206
Senior Researcher
Doctor of physico-mathematical sciences
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 27.04.1964
E-mail:
   
Main publications:
  1. Tarasev A.M., Uspenskii A.A., Ushakov V.N., “Approksimatsionnye skhemy i konechno-raznostnye operatory dlya postroeniya obobschennykh reshenii uravnenii Gamiltona-Yakobi”, Izvestiya RAN. Tekhnicheskaya kibernetika, 1994, № 3, 173-185
  2. Uspenskii A.A., “Proizvodnye v silu diffeomorfizmov i ikh prilozheniya v teorii upravleniya i geometricheskoi optike”, Trudy Instituta matematiki i mekhaniki, 21:2 (2015), 252-266
  3. Ushakov V.N., Uspenskii A.A., “Alfa-mnozhestva v konechnomernykh evklidovykh prostranstvakh i ikh svoistva”, Vestnik Udmurtskogo universiteta. Matematika.Mekhanika. Kompyuternye nauki., 26:1 (2016), 95-120

https://www.mathnet.ru/eng/person18447
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/319346
https://elibrary.ru/author_items.asp?spin=1491-4686
https://orcid.org/0000-0003-0725-4233
https://www.webofscience.com/wos/author/record/J-3594-2017

Publications in Math-Net.Ru Citations
2024
1. P. D. Lebedev, A. A. Uspenskii, “Newton's method in constructing a singular set of a minimax solution in a class of boundary value problems for the Hamilton — Jacobi equations”, Chelyab. Fiz.-Mat. Zh., 9:1 (2024),  63–76  mathnet
2. P. D. Lebedev, A. A. Uspenskii, “On smoothness conditions and selection of the edge of a scattering surface in one class of 3D time-optimal problems”, Izv. IMI UdGU, 63 (2024),  37–48  mathnet
3. P. D. Lebedev, A. A. Uspenskii, “Numerical-analytical construction of a generalized solution of the eikonal equation in the plane case”, Mat. Sb., 215:9 (2024),  99–124  mathnet
4. A. A. Uspenskii, P. D. Lebedev, “Alpha sets and their hulls: analytical relationships in the plane case”, Russian Universities Reports. Mathematics, 29:146 (2024),  204–217  mathnet
2022
5. Pavel D. Lebedev, Alexander A. Uspenskii, “Combined algorithms for constructing a solution to the time-optimal problem in three-dimensional space based on the selection of extreme points of the scattering surface”, Ural Math. J., 8:2 (2022),  115–126  mathnet  mathscinet  elib 1
2021
6. P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov, “Iterative algorithms for minimizing the Hausdorff distance between convex polyhedrons”, Izv. IMI UdGU, 57 (2021),  142–155  mathnet
7. P. D. Lebedev, A. A. Uspenskii, “On the analytical construction of solutions for one class of time-optimal control problems with nonconvex target set”, Trudy Inst. Mat. i Mekh. UrO RAN, 27:3 (2021),  128–140  mathnet  elib 2
8. A. A. Uspenskii, P. D. Lebedev, “On singularity structure of minimax solution to Dirichlet problem for eikonal type equation with discontinuous curvature of boundary of boundary set”, Ufimsk. Mat. Zh., 13:3 (2021),  129–154  mathnet; Ufa Math. J., 13:3 (2021), 126–151  isi  scopus 2
9. A. A. Uspenskii, P. D. Lebedev, “On the structure of the singular set of solutions in one class of 3D time-optimal control problems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:3 (2021),  471–486  mathnet  elib 2
2020
10. P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov, “Algorithms of minimization of Hausdorff deviation of a convex compact from a set of movable convex polygons”, Chelyab. Fiz.-Mat. Zh., 5:2 (2020),  218–232  mathnet 1
11. P. D. Lebedev, V. N. Ushakov, A. A. Uspenskii, “Numerical methods for constructing suboptimal packings of nonconvex domains with curved boundary”, Diskretn. Anal. Issled. Oper., 27:4 (2020),  58–79  mathnet; J. Appl. Industr. Math., 14:4 (2020), 681–692  scopus 3
12. P. D. Lebedev, A. A. Uspenskii, “Construction of scattering curves in one class of time-optimal control problems with leaps of a target set boundary curvature”, Izv. IMI UdGU, 55 (2020),  93–112  mathnet 4
13. A. A. Uspenskii, P. D. Lebedev, “Properties of non stationer pseudo vertex with the break of smoothness of the target set boarder curvature in the Dirichlet problem to eikonal type equation”, Sib. Èlektron. Mat. Izv., 17 (2020),  2028–2044  mathnet 1
14. P. D. Lebedev, A. A. Uspenskii, “Elements of analytical solutions constructor in a class of time-optimal control problems with the break of curvature of a target set”, Russian Universities Reports. Mathematics, 25:132 (2020),  370–386  mathnet 1
2019
15. P. D. Lebedev, A. A. Uspenskii, “Algorithms for solving the velocity problem with circular vectogram in inhomogeneous medium”, Chelyab. Fiz.-Mat. Zh., 4:4 (2019),  387–397  mathnet  elib
16. P. D. Lebedev, A. A. Uspenskii, “Construction of a solution to a velocity problem in the case of violation of the smoothness of the curvature of the target set boundary”, Izv. IMI UdGU, 53 (2019),  98–114  mathnet  elib 6
17. P. D. Lebedev, A. A. Uspenskii, “Construction of a nonsmooth solution in a time-optimal problem with a low order of smoothness of the boundary of the target set”, Trudy Inst. Mat. i Mekh. UrO RAN, 25:1 (2019),  108–119  mathnet  elib 9
2018
18. V. N. Ushakov, A. A. Uspenskii, A. A. Ershov, “Alpha-sets in finite-dimensional Euclidean spaces and their applications in control theory”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 14:3 (2018),  261–272  mathnet  elib 2
19. A. A. Uspenskii, P. D. Lebedev, “Euclidean distance to a closed set as a minimax solution of the Dirichlet problem for the Hamilton-Jacobi equation”, Tambov University Reports. Series: Natural and Technical Sciences, 23:124 (2018),  797–804  mathnet  elib
20. A. A. Uspenskii, P. D. Lebedev, “Identification of the singularity of the generalized solution of the Dirichlet problem for an eikonal type equation under the conditions of minimal smoothness of a boundary set”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:1 (2018),  59–73  mathnet  elib 11
2017
21. A. A. Uspenskii, “Weak invariance of a cylindrical set with smooth boundary with respect to a control system”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:1 (2017),  241–250  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 164–172  isi
2016
22. V. N. Ushakov, A. A. Uspenskii, “Theorems on the separability of $\alpha$-sets in Euclidean space”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:2 (2016),  277–291  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 231–245  isi  scopus 3
23. P. D. Lebedev, A. A. Uspenskii, “Construction of the optimal result function and dispersing lines in time-optimal problems with a nonconvex target set”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:2 (2016),  188–198  mathnet  mathscinet  elib 5
24. A. A. Uspenskii, P. D. Lebedev, “The construction of singular curves for generalized solutions of eikonal-type equations with a curvature break in the boundary of the boundary set”, Trudy Inst. Mat. i Mekh. UrO RAN, 22:1 (2016),  282–293  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 191–202  isi  scopus 5
25. V. N. Ushakov, A. A. Uspenskii, “$\alpha$-sets in finite dimensional Euclidean spaces and their properties”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:1 (2016),  95–120  mathnet  mathscinet  elib 16
2015
26. A. A. Uspenskii, “Derivatives by virtue of diffeomorphisms and their applications in control theory and geometrical optics”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:2 (2015),  252–266  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 238–253  isi  scopus 2
27. A. A. Uspenskii, “Necessary conditions for the existence of pseudovertices of the boundary set in the Dirichlet problem for the eikonal equation”, Trudy Inst. Mat. i Mekh. UrO RAN, 21:1 (2015),  250–263  mathnet  mathscinet  elib 12
2014
28. A. A. Uspenskii, “Calculation formulas for nonsmooth singularities of the optimal result function in a time-optimal problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 20:3 (2014),  276–290  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 239–254  isi  scopus 14
2013
29. A. A. Uspenskii, P. D. Lebedev, P. A. Vasev, “Approximation of nonsmooth optimal result in one class of velocity problems”, Vestnik Chelyabinsk. Gos. Univ., 2013, no. 16,  71–77  mathnet
30. V. N. Ushakov, A. A. Uspenskiy, P. D. Lebedev, “Geometry of singular curves for one class of velocity”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2013, no. 3,  157–167  mathnet 11
31. P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov, “Algorithms of the best approximations of the flat sets by the union of circles”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4,  88–99  mathnet 6
2012
32. V. N. Ushakov, A. A. Uspenskii, “Stability defect of maximal stable bridge in approaching game problem with closed target”, Izv. IMI UdGU, 2012, no. 1(39),  140  mathnet
2011
33. V. N. Ushakov, A. A. Uspenskii, A. G. Malev, “Estimate of the stability defect for a positional absorption set subjected to discriminant transformations”, Trudy Inst. Mat. i Mekh. UrO RAN, 17:2 (2011),  209–224  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 279, suppl. 1 (2012), 113–129  isi  scopus 8
2010
34. Vladimir N. Ushakov, Alexandr A. Uspenskiy, “Function defect in differential games with terminal pay”, Mat. Teor. Igr Pril., 2:2 (2010),  99–128  mathnet  elib 1
35. A. A. Uspenskii, P. D. Lebedev, “On the set of limit values of local diffeomorphisms in wavefront evolution”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:1 (2010),  171–185  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S255–S270  isi  scopus 16
36. V. N. Ushakov, A. A. Uspenskii, “On a supplement to the stability property in differential games”, Trudy Mat. Inst. Steklova, 271 (2010),  299–318  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 271 (2010), 286–305  isi  scopus 10
37. A. A. Uspenskii, P. D. Lebedev, “Singularities' of Optimal-Time Function in One Class of Optimal-Time Control Problems Construction Algorithms”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 3,  30–41  mathnet 2
2009
38. A. A. Uspenskii, P. D. Lebedev, “Construction of the optimal outcome function for a time-optimal problem on the basis of a symmetry set”, Avtomat. i Telemekh., 2009, no. 7,  50–57  mathnet  mathscinet  zmath  elib; Autom. Remote Control, 70:7 (2009), 1132–1139  isi  elib  scopus 21
39. P. D. Lebedev, A. A. Uspenskii, “Procedures for calculating the nonconvexity measures of a plane set”, Zh. Vychisl. Mat. Mat. Fiz., 49:3 (2009),  431–440  mathnet  mathscinet  elib; Comput. Math. Math. Phys., 49:3 (2009), 418–427  isi  elib  scopus 8
2008
40. P. D. Lebedev, A. A. Uspenskii, “Geometry and the asymptotics of wave forms”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 3,  27–37  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 52:3 (2008), 24–33 22
41. P. D. Lebedev, A. A. Uspenskii, “Условия трансверсальности ветвей решения нелинейного уравнения в задаче быстродействия с круговой индикатрисой”, Trudy Inst. Mat. i Mekh. UrO RAN, 14:4 (2008),  82–99  mathnet  elib 12
42. P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov, “Construction of a minimax solution for an eikonal-type equation”, Trudy Inst. Mat. i Mekh. UrO RAN, 14:2 (2008),  182–191  mathnet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 263, suppl. 2 (2008), S191–S201  isi  scopus 33
43. A. A. Uspenskii, P. D. Lebedev, “Construction of the function of the best result for the system with simple dynamic”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2008, no. 2,  152–154  mathnet  elib 1
2006
44. P. D. Lebedev, A. A. Uspenskii, “On the geometry of wave fronts”, Izv. IMI UdGU, 2006, no. 3(37),  79–80  mathnet 2
2005
45. S. V. Grigor'eva, V. Yu. Pakhotinskikh, A. A. Uspenskii, V. N. Ushakov, “Construction of solutions in certain differential games with phase constraints”, Mat. Sb., 196:4 (2005),  51–78  mathnet  mathscinet  zmath  elib; Sb. Math., 196:4 (2005), 513–539  isi  elib  scopus 21
2004
46. V. N. Ushakov, A. A. Uspenskii, T. B. Tokmantsev, “Stable bridges in differential games in a finite time interval”, Trudy Inst. Mat. i Mekh. UrO RAN, 10:2 (2004),  155–177  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2004no. , suppl. 2, S168–S192 2
2000
47. S. V. Grigor'eva, A. M. Tarasyev, A. A. Uspenskii, V. N. Ushakov, “Constructions of the differential game theory for solving the Hamilton–Jacobi equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 6:2 (2000),  320–336  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2000no. , suppl. 2, S38–S53

Presentations in Math-Net.Ru
1. Элементы аналитического конструктора решений в классе задач управления с целевым множеством с разрывной кривизной границы (20 мин)
П. Д. Лебедев, А. А. Успенский
International Scientific Conference KOLMOGOROV READINGS – IX. General Control Problems and their Applications (GCP–2020), dedicated to the 70-th birth anniversary of Alexander Ivanovich Bulgakov and to the 90-th anniversary of the Institute of Mathematics, Physics and Information Technologies of Derzhavin Tambov State University
October 13, 2020 16:25   

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