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Gamkrelidze, Revaz Valer'yanovich
Total publications: 91 (69)
in MathSciNet: 85 (73)
in zbMATH: 68 (60)
in Web of Science: 27 (19)
in Scopus: 27 (25)
Cited articles: 39
Citations: 649
Presentations: 10

Number of views:
This page:11009
Abstract pages:29040
Full texts:11258
References:919
Member of the Russian Academy of Sciences
Professor
Doctor of physico-mathematical sciences (1961)
Speciality: 01.01.00 (Mathematics)
E-mail:
Keywords: Chern characteristic classes and their computation for complex algebraic manifolds, linear optimal control systems, Pontryagin maximum principle, optimal control with phase constraints, sliding optimal states
UDC: 517.938, 517.317, 519.3, 51, (091), 517.977.52, 517.9, 517.977.5, 514.7, 517.977

Subject:

Algebraic topology and characteristic classes, optimal control and calculus of variations
   
Main publications:
  1. R.V. Gamkrelidze, “Tsikly Cherna kompleksnykh algebraicheskikh mnogoobrazii”, Izvestiya AN SSSR seriya matematicheskaya, 20:4 (1956), 685-706
  2. V.G. Boltyanskii, R.V. Gamkrelidze, L.S. Pontryagin, “K teorii optimalnykh protsessov”, DAN SSSR, 110:1 (1956), 7-10
  3. R.V. Gamkrelidze, “Teoriya optimalnykh po bystrodeistviyu protsessov v lineinykh sistemakh”, Izvestiya AN SSSR seriya matematicheskaya, 22 (1958), 449-474
  4. R.V. Gamkrelidze, “Optimalnye protsessy upravleniya pri ogranichennykh fazovykh koordinatakh”, Izvestiya AN SSSR seriya matematicheskaya, 24 (1960), 315-356
  5. R.V. Gamkrelidze, “O skolzyaschikh optimalnykh rezhimakh”, DAN SSSR, 143:6 (1962), 1243-1245

https://www.mathnet.ru/eng/person18956
https://ru.wikipedia.org/wiki/Gamkrelidze,_Revaz_Valerianovich
https://scholar.google.com/citations?user=S-YInwkAAAAJ&hl=en
https://zbmath.org/authors/ai:gamkrelidze.revaz-v
https://mathscinet.ams.org/mathscinet/MRAuthorID/190428
https://elibrary.ru/author_items.asp?authorid=1868
https://www.webofscience.com/wos/author/record/T-7015-2017
https://www.scopus.com/authid/detail.url?authorId=6506468968

Full list of publications:
| scientific publications | by years | by types | by times cited | common list |


Citations (Crossref Cited-By Service + Math-Net.Ru)

   2022
1. R. V. Gamkrelidze, A. V. Ovchinnikov, “Dual formulation of the lemma on substitution homomorphisms”, Dokl. Math., 106:1 (2022), 218–219  mathnet  crossref  crossref  elib

   2019
2. R. V. Gamkrelidze, “History of the Discovery of the Pontryagin Maximum Principle”, Proc. Steklov Inst. Math., 304 (2019), 1–7  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
3. R. V. Gamkrelidze, Osnovy optimalnogo upravleniya, Izd. 3, ispr., URSS, 2019 , 200 pp.

   2015
4. R. V. Gamkrelidze, “Dual Formulation of the Pontryagin Maximum Principle in Optimal Control”, Proc. Steklov Inst. Math., 291 (2015), 61–67  mathnet  crossref  crossref  isi  elib  elib  scopus

   2014
5. R. V. Gamkrelidze, “Differential-geometric and invariance properties of the equations of Maximum Principle (MP)”, Geometric Control Theory and Sub-Riemannian Geometry, Springer INdAM Series, 5, Springer, 2014, 167–175  crossref  mathscinet  zmath  isi  elib  scopus 1
6. “Dvoistvennaya formulirovka printsipa maksimuma Pontryagina (PMP)”, Sedmaya mezhdunarodnaya konferentsiya po differentsialnym i funktsionalno-differentsialnym uravneniyam. Mezhdunarodnyi seminar «Prostranstvenno-vremennye dinamicheskie sistemy», Tezisy dokladov (Moskva, 22–29 avgusta 2014 g.), Rossiiskii universitet druzhby narodov, M., 2014, 134–136  elib

   2011
7. A. A. Agrachev, R. V. Gamkrelidze, “The geometry of maximum principle”, Proc. Steklov Inst. Math., 273 (2011), 1–22  mathnet  crossref  mathscinet  zmath  isi  elib

   2010
8. R. V. Gamkrelidze, “The Pontryagin derivative in optimal control”, Proc. Steklov Inst. Math., 268 (2010), 87–92  mathnet  crossref  mathscinet  zmath  zmath  isi  elib  elib  elib  scopus

   2009
9. R. V. Gamkrelidze, “Hamiltonian form of the maximum principle”, Control Cybernet., 38:4A (2009), 959–971  mathscinet  zmath  isi  elib  scopus

   2008
10. R. V. Gamkrelidze, ““The Pontryagin derivative” in optimal control”, Dokl. Math., 77:3 (2008), 329–331  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus

   2006
11. R. V. Gamkrelidze, “Discovery of the maximum principle”, Mathematical events of the twentieth century, Springer-Verlag, Berlin, 2006, 85–99  crossref  mathscinet  zmath 4
12. A. A. Agrachev, R. V. Gamkrelidze, “The Pontryagin Maximum Principle 50 years later”, Proc. Inst. Math. Mech., 253, suppl. 1 (2006), S4–S12  mathnet  crossref  mathscinet  zmath  elib  scopus
13. J. Math. Sci. (N. Y.), 135:4 (2006), 3093–3108  crossref  mathscinet  zmath  scopus

   1999
14. R. V. Gamkrelidze, “Discovery of the maximum principle”, J. Dynam. Control Systems, 5:4 (1999), 437–451  crossref  mathscinet  zmath  elib  scopus 26
15. R. V. Gamkrelidze, “Mathematical Work of L. S. Pontryagin”, Proc. Steklov Inst. Math., 224 (1999), 8–19  mathnet  mathscinet  zmath

   1998
16. A. Agrachev, R. Gamkrelidze, “Symplectic methods for optimization and control”, Geometry of feedback and optimal control, Monogr. Textbooks Pure Appl. Math., 207, Dekker, New York, 1998, 19–77  mathscinet  zmath

   2000
17. R. V. Gamkrelidze, “The mathematical work of L. S. Pontryagin”, J. Math. Sci. (New York), 100:5 (2000), 2447–2457  mathnet  crossref  mathscinet  zmath

   1997
18. A. A. Agrachev, R. V. Gamkrelidze, “Feedback-invariant optimal control theory and differential geometry. I. Regular extremals”, J. Dynam. Control Systems, 3:3 (1997), 343–389  crossref  mathscinet  zmath  elib  scopus 60

   1995
19. A. A. Agrachev, R. V. Gamkrelidze, “On the orbits of groups of diffeomorphisms and flows”, Proc. Steklov Inst. Math., 209 (1995), 1–10  mathnet  mathscinet  zmath

   1994
20. A. A. Agrachëv, R. V. Gamkrelidze, “The shuffle product and symmetric groups”, Differential equations, dynamical systems, and control science, Lecture Notes in Pure and Appl. Math., 152, Dekker, New York, 1994, 365–382  mathscinet  zmath  isi

   1993
21. A. A. Agrachëv, R. V. Gamkrelidze, “Local controllability and semigroups of diffeomorphisms”, Acta Appl. Math., 32:1 (1993), 1–57  crossref  mathscinet  zmath  isi  elib  scopus 24
22. A. A. Agrachëv, R. V. Gamkrelidze, “Local controllability for families of diffeomorphisms”, Systems Control Lett., 20:1 (1993), 67–76  crossref  mathscinet  zmath  isi  elib  scopus 6

   1994
23. A. A. Agrachev, R. V. Gamkrelidze, “Volterra series and permutation groups”, J. Math. Sci., 71:3 (1994), 2409–2433  mathnet  crossref  mathscinet  zmath  scopus

   1992
24. A. A. Agrachev, R. V. Gamkrelidze, “Symplectic geometry and conditions necessary conditions for optimality”, Math. USSR-Sb., 72:1 (1992), 29–45  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus

   1990
25. Soviet Math. Dokl., 41:2 (1990), 227–231 (1991)  mathnet  mathscinet  zmath  isi
26. A. A. Agrachëv, R. V. Gamkrelidze, “Symplectic geometry for optimal control”, Nonlinear controllability and optimal control, Monogr. Textbooks Pure Appl. Math., 133, Dekker, New York, 1990, 263–277  mathscinet  zmath  isi

   1989
27. A. A. Agrachëv, R. V. Gamkrelidze, A. V. Sarychev, “Local invariants of smooth control systems”, Acta Appl. Math., 14:3 (1989), 191–237  crossref  mathscinet  zmath  isi  elib  scopus 70

   1991
28. A. A. Agrachev, R. V. Gamkrelidze, “Quadratic mappings and smooth vector functions: Euler characteristics of level sets”, J. Soviet Math., 55:4 (1991), 1892–1928  mathnet  crossref  mathscinet  zmath  scopus
29. A. A. Agrachev, R. V. Gamkrelidze, “Quasi-extremality for controllable systems”, J. Soviet Math., 55:4 (1991), 1849–1864  mathnet  crossref  mathscinet  zmath  scopus
30. R. V. Gamkrelidze, A. A. Agrachev, S. A. Vakhrameev, “Ordinary differential equations on vector bundles, and chronological calculus”, J. Soviet Math., 55:4 (1991), 1777–1848  mathnet  crossref  mathscinet  zmath  scopus

   1988
31. Soviet Math. Dokl., 37:2 (1988), 297–300  mathnet  mathscinet  zmath  isi

   1986
32. L. S. Pontryagin, V. G. Boltyanskiĭ, R. V. Gamkrelidze, E. F. Mishchenko, Selected works, v. 4, Classics of Soviet Mathematics, The mathematical theory of optimal processes, Gordon & Breach Science Publishers, New York, 1986 , xxiv+360 pp.  mathscinet
33. A. A. Agrachëv, R. V. Gamkrelidze, “Morse and Maslov indices for the extremals of controllable systems”, Dokl. Akad. Nauk SSSR, 287:3 (1986), 521–524  mathnet  mathscinet  zmath  isi

   1985
34. A. A. Agrachëv, R. V. Gamkrelidze, “The index of extremality and quasiextremal controls”, Dokl. Akad. Nauk SSSR, 284:4 (1985), 777–781  mathnet  mathscinet  zmath  isi 3

   1986
35. R. V. Gamkrelidze, “Sliding modes in optimal control theory”, Proc. Steklov Inst. Math., 169 (1986), 185–198  mathnet  mathscinet  zmath
36. D. V. Anosov, R. V. Gamkrelidze, E. F. Mishchenko, M. M. Postnikov, “The mathematical work of L. S. Pontryagin”, Proc. Steklov Inst. Math., 166 (1986), 1–15  mathnet  mathscinet  zmath

   1983
37. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mischenko, Matematicheskaya teoriya optimalnykh protsessov, 4-e izd., Nauka, M., 1983 , 392 pp.  mathscinet  zmath

   1985
38. A. A. Agrachev, S. A. Vakhrameev, R. V. Gamkrelidze, “Differential geometric and group theoretic methods in optimal control theory”, J. Soviet Math., 28:2 (1985), 145–182  mathnet  crossref  mathscinet  zmath  scopus

   1981
39. A. A. Agrachev, R. V. Gamkrelidze, “Chronological algebras and nonstationary vector fields”, J. Soviet Math., 17:1 (1981), 1650–1675  mathnet  crossref  mathscinet  zmath  scopus

   1979
40. R. V. Gamkrelidze, “Exponential representation of solutions of ordinary differential equations”, Equadiff IV, Proc. Czechoslovak Conf. Differential Equations and their Applications (Prague, 1977), Lecture Notes in Math., 703, Springer, Berlin, 1979, 118–129  crossref  mathscinet 6

   1978
41. L. Pontriaguine, V. Boltianski, R. Gamkrélidzé, E. Michtchenko, Théorie mathématique des processus optimaux, Traduit du russe par Djilali Embarek; Unaltered reprint, Mir, Moscow, 1978 , 317 pp.  mathscinet

   1979
42. A. A. Agrachev, R. V. Gamkrelidze, “The exponential representation of flows and the chronological calculus”, Math. USSR-Sb., 35:6 (1979), 727–785  mathnet  crossref  mathscinet  zmath  isi  scopus

   1976
43. A. A. Agrachev, R. V. Gamkrelidze, “A second order optimality principle for a time-optimal problem”, Math. USSR-Sb., 29:4 (1976), 547–576  mathnet  crossref  mathscinet  zmath  isi  scopus

   1975
44. R. V. Gamkrelidze, Osnovy optimalnogo upravleniya, Izd-vo Tbilisskogo un-ta, Tbilisi, 1975 , 230 pp.  mathscinet; Р. В. Гамкрелидзе, Основы оптимального управления, Изд-во Тбилисского ун-та, Тбилиси, 1977 , 254 с.  mathscinet  zmath; R. V. Gamkrelidze, Principles of optimal control theory, Mathematical Concepts and Methods in Science and Engineering, 7, Plenum Press, New York, 1978 , xii+175 pp.  mathscinet  zmath

   1974
45. R. V. Gamkrelidze, G. L. Kharatishvili, “A differential game of evasion with nonlinear control”, SIAM J. Control, 12 (1974), 332–349  crossref  mathscinet  zmath  scopus 15
46. L. Pontriaguine, V. Boltianski, R. Gamkrelidze, E. Michtchenko, Théorie mathématique des processus optimaux, Mir, Moscow, 1974 , 317 pp.  mathscinet  zmath

   1971
47. R. V. Gamkrelidze, Kharatishvili G. L., “Conditions nécessaires du premier ordre dans les problèmes d'extremum”, Actes du Congrès International des Mathématiciens (Nice, 1970), Gauthier-Villars, Paris, 1971, 169–176  mathscinet
48. R. V. Gamkrelidze, “Necessary first order conditions, and the axiomatics of extremal problems”, Proc. Steklov Inst. Math., 112 (1971), 156–186  mathnet  mathscinet  zmath

   1969
49. R. V. Gamkrelidze, G. L. Kharatishvili, “Extremal problems in linear topological spaces”, Math. USSR-Izv., 3:4 (1969), 737–794  mathnet  crossref  mathscinet  zmath

   1967
50. Gamkrelidze Revaz V., “Extremal problems in finite-dimensional spaces”, J. Optimization Theory Appl., 1 (1967), 173–193  crossref  mathscinet  zmath  elib  scopus 5
51. R. V. Gamkrelidze, Kharatishvili G. L., “Extremal problems in linear topological spaces. I”, Math. Systems Theory, 1 (1967), 229–256  crossref  mathscinet  zmath  scopus 18
52. R. V. Gamkrelidze, G. L. Haratišvili, “The theory of the first variation in extremal problems”, Sakharth. SSR Mecn. Akad. Moambe, 46 (1967), 27–31  mathscinet  zmath

   1965
53. R. V. Gamkrelidze, “On some extremal problems in the theory of differential equations with applications to the theory of optimal control”, J. Soc. Indust. Appl. Math. Ser. A Control, 3 (1965), 106–128  crossref  mathscinet  zmath 64
54. R. V. Gamkrelidze, “On a theory of the first variation”, Dokl. Akad. Nauk SSSR, 161 (1965), 23–26  mathnet  mathscinet  mathscinet  zmath 1

   1964
55. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishchenko, The mathematical theory of optimal processes, A Pergamon Press Book, The Macmillan Co., New York, 1964 , vii+338 pp.  mathscinet  zmath

   1963
56. L. S. Pontrjagin, V. G. Boltjanskiĭ, R. V. Gamkrelidze, E. F. Miščenko, “The mathematical theory of optimal processes”, Proc. 4th All-Union Math. Congr. (Leningrad, 1961), Izdat. Akad. Nauk SSSR, Leningrad, 1963, 214–218  mathscinet

   1962
57. R. V. Gamkrelidze, “On sliding optimal states”, Dokl. Akad. Nauk SSSR, 143 (1962), 1243–1245  mathnet  mathscinet  mathscinet  zmath 17

   1961
58. V. G. Boltyanski, R. V. Gamkrelidze, E. F. Mishchenko, L. S. Pontryagin, “The maximum principle in the theory of optimal processes of control (with discussion)”, Automatic and Remote Control, Proc. First Internat. Congr. Internat. Fed. Automat. Control (Moscow, 1960), Vol. I, Butterworths, London, 1961, 454–459  mathscinet
59. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mischenko, Matematicheskaya teoriya optimalnykh protsessov, Fizmatlit, M., 1961 , 391 pp.  mathscinet; L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishchenko, The mathematical theory of optimal processes, ed. L. W. Neustadt, Interscience Publishers John Wiley & Sons, Inc., New York–London, 1962 , viii+360 pp.  mathscinet  zmath; L. S. Pontrjagin, V. G. Boltjanskij, R. V. Gamkrelidze, E. F. Miščenko, Mathematische Theorie optimaler Prozesse, R. Oldenbourg, Munich–Vienna, 1964 , 340 pp.  mathscinet
60. V. G. Boltjanskiĭ, R. V. Gamkrelidze, L. S. Pontryagin, “The theory of optimal processes. I. The maximum principle”, Amer. Math. Soc. Transl. (2), 18 (1961), 341–382  mathscinet

   1960
61. R. V. Gamkrelidze, “Optimal control processes for bounded phase coordinates”, Izv. Akad. Nauk SSSR Ser. Mat., 24:3 (1960), 315–356  mathnet  mathscinet  zmath
62. V. G. Boltyanskii, R. V. Gamkrelidze, L. S. Pontryagin, “Theory of optimal processes. I. The maximum principle”, Izv. Akad. Nauk SSSR Ser. Mat., 24:1 (1960), 3–42  mathnet  mathscinet  zmath

   1959
63. R. V. Gamkrelidze, “Optimum-rate processes with bounded phase coordinates”, Dokl. Akad. Nauk SSSR, 125 (1959), 475–478  mathscinet  zmath

   1958
64. R. V. Gamkrelidze, “On the general theory of optimal processes”, Dokl. Akad. Nauk SSSR, 123 (1958), 223–226  mathnet  mathscinet  mathscinet  zmath
65. R. V. Gamkrelidze, “Theory of processes in linear systems which are optimal with respect to rapidity of action”, Izv. Akad. Nauk SSSR Ser. Mat., 22:4 (1958), 449–474  mathnet  mathscinet  zmath

   1957
66. R. V. Gamkrelidze, “On the theory of optimal processes in linear systems”, Dokl. Akad. Nauk SSSR (N.S.), 116 (1957), 9–11  mathnet  mathscinet  mathscinet  zmath 2

   1956
67. V. G. Boltyanskiĭ, R. V. Gamkrelidze, L. S. Pontryagin, “On the theory of optimal processes”, Dokl. Akad. Nauk SSSR (N.S.), 110 (1956), 7–10  mathscinet  zmath
68. R. V. Gamkrelidze, “Chern's cycles of complex algebraic manifolds”, Izv. Akad. Nauk SSSR Ser. Mat., 20:5 (1956), 685–706  mathnet  mathscinet  zmath

   1953
69. R. V. Gamkrelidze, “Computation of the Chern cycles of algebraic manifolds”, Doklady Akad. Nauk SSSR (N.S.), 90 (1953), 719–722  mathscinet  zmath

Presentations in Math-Net.Ru
1. History of the discovery of the Pontryagin maximum principle
R. V. Gamkrelidze
International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin
December 12, 2018 09:45   
2. Гамильтонов подход в экстремальных задачах управления
R. V. Gamkrelidze
Hamiltonian systems and statistical mechanics
December 14, 2015
3. О двойственной формулировке принципа максимума Понтрягина
R. V. Gamkrelidze
Problems of Mathematical Control Theory
October 24, 2014 14:00
4. Dual formulation of the Pontryagin maximum principle (PMP)
R. V. Gamkrelidze
The Seventh International Conference on Differential and Functional Differential Equations
August 23, 2014 15:05   
5. Memoirs about L. S. Pontryagin
Yu. S. Ledyaev, R. V. Gamkrelidze
Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin
September 24, 2013 18:00   
6. Canonical duality in problems of time optimal control
R. V. Gamkrelidze
Conference "Optimal Control and Applications" dedicated to the 105th anniversary of Lev Semenovich Pontryagin
September 24, 2013 10:20   
7. Инвариантное представление принципа максимума
R. V. Gamkrelidze
Conference "Differential Equations and Optimal Control", dedicated to the 90th anniversary of E. F. Mishchenko
April 16, 2012 11:05   
8. Первоначальная форма принципа максимума Понтрягина
R. V. Gamkrelidze
Seminar "Optimal Control and Dynamical Systems"
March 17, 2010 12:00
9. О гамильтоновой форме принципа максимума Понтрягина
R. V. Gamkrelidze
Seminar "Optimal Control and Dynamical Systems"
February 17, 2010 12:00
10. Hamiltonian format of Pontryagin's maximum principle
R. V. Gamkrelidze
International Conference "Differential Equations and Topology" dedicated to the Centennial Anniversary of L. S. Pontryagin
June 18, 2008 10:20   

Books in Math-Net.Ru
  1. Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 304, ed. R. V. Gamkrelidze, S. M. Aseev, M. S. Nikol'skii, 2019, 328 с.
    http://mi.mathnet.ru/book1743
  2. Mathematical control theory and differential equations, Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 277, ed. R. V. Gamkrelidze, A. G. Sergeev, 2012, 287 с.
    http://mi.mathnet.ru/book1463
  3. Optimal control and differential equations, Collection of articles. To the seventieth birthday of academician E. F. Mishchenko, Trudy Mat. Inst. Steklov., 211, ed. E. F. Mishchenko, R. V. Gamkrelidze, 1995, 526 с.
    http://mi.mathnet.ru/book1065
  4. Selected topics in the theory of oscillations and optimal control theory, Trudy Mat. Inst. Steklov., 197, ed. R. V. Gamkrelidze, E. F. Mishchenko, 1991, 168 с.
    http://mi.mathnet.ru/book1109
  5. Itogi Nauki i Tekhniki. Ser. Algebra. Topol. Geom., 29, ed. R. V. Gamkrelidze, 1991, 193 с.
    http://mi.mathnet.ru/book40
  6. Itogi Nauki. Ser. Mat. Algebra. Topol. Geom. 1967, ed. R. V. Gamkrelidze, 1969, 228 с.
    http://mi.mathnet.ru/book44
  7. Itogi Nauki. Algebra. Topol. 1962, ed. R. V. Gamkrelidze, 1963, 224 с.
    http://mi.mathnet.ru/book19

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