Agrachev, Andrei Alexandrovich

Total publications: 141 (136)
in MathSciNet: 132 (128)
in zbMATH: 110 (108)
in Web of Science: 77 (74)
in Scopus: 94 (94)
Cited articles: 119
Citations in Math-Net.Ru: 265
Citations in Web of Science: 1178
Citations in Scopus: 1686
Presentations: 27

Number of views:
This page:8000
Abstract pages:16527
Full texts:4824
Doctor of physico-mathematical sciences (1989)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 29.03.1952
Phone: +7 (495) 984 81 41 * 39 35
Fax: +7 (499) 135 05 55
E-mail: ,
Keywords: geometric control theory, optimal control, symplectic geometry, singularities theory.
UDC: 514.7, 517.317, 517.5, 517.938, 517.977.1, 519.3, 517.9, 517.97, 517.977


Mathematical control theory, sub-Riemannian geometry and and related topics in dynamical systems, geometry and topology.

Main publications:
  1. Agrachev A. A., Gauthier J.-P., “On subanalyticity of Carnot–Caratheodory distances”, Annales de lInst. Henry Poincare – Analyse non lineaire, 18 (2001), 359–382  crossref  mathscinet  zmath
  2. Agrachev A. A. Sarychev A. V., “Controllability of 2D Euler and Navier–Stokes equations by degenerate forcing”, Commun. Math. Phys., 265 (2006), 673–697
  3. Agrachev A. A., “Well-posed infinite horizon variational problems on a compact manifold”, Proceed. Steklov Math. Inst., 268 (2010), 24–39
  4. Agrachev A. A., Lerario A., “Systems of quadratic inequalities”, Proceedings of the London Math. Soc., 105 (2012), 622–660
  5. Agrachev A. A., Barilari D., Rizzi L., “Curvature: A variational approach”, Memoirs of the American Math. Soc., 256 (2018), 1–116
List of publications on Google Scholar

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

1. A. Agrachev, B. Beschatnyj, “Jacobi fields in optimal control: one-dimensional variations”, J. Dynamical and Control Systems (to appear)
2. A. Agrachev, A. Sarychev, “Control in the space of ensembles of points”, SIAM J. on Control and Optimization (to appear)

3. A. Agrachev, D. Barilari, U. Boscain, A comprehensive introduction to sub-Riemannian geometry, Cambridge University Press, 2020 , 763 pp.  mathscinet
4. A. Agrachev, K. Kozhasov, A. Uschmajew, “Chebyshev polynomials and best rank-one approximation ratio”, SIAM J. Matrix Anal. Appl., 41 (2020), 308–331  crossref

5. A. A. Agrachev, “Spectrum of the Second Variation”, Proc. Steklov Inst. Math., 304 (2019), 26–41  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
6. A. A. Agrachev, D. Barilari, E. Paoli, “Volume geodesic distortion and ricci curvature for Hamiltonian dynamics”, Ann. Inst. Fourier (Grenoble), 69:3 (2019), 1187–1228 , arXiv: 1602.08745  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1);
7. A. A. Agrachev, “Optimalnoe upravlenie”, Matematicheskaya sostavlyayuschaya, 2-e izd., rassh. i dop., eds. N. N. Andreev, S. P. Konovalov, N. M. Panyunin, Matematicheskie etyudy, M., 2019, 26  zmath

8. A. Agrachev, D. Barilari, L. Rizzi, Curvature: a variational approach, Mem. Amer. Math. Soc., 256, Amer. Math. Soc., Providence, RI, 2018 , 116 pp., arXiv: 1306.5318  scopus (cited: 35)
9. Andrei A. Agrachev, Carolina Biolo, “Switching in time-optimal problem with control in a ball”, SIAM J. Control Optim., 156:1 (2018), 183–200  mathnet  crossref  mathscinet  isi  scopus
10. Andrei Agrachev, Ugo Boscain, Robert Neel, Luca Rizzi, “Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling”, ESAIM: COCV, 24:3 (2018), 1075–1105  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 3)
11. Andrei A. Agrachev, Carolina Biolo, “Optimality of broken extremals”, J. Dyn. Control Syst., 25:2 (2018), 289–307  mathnet  crossref  mathscinet  isi  scopus

12. Andrei Agrachev, Davide Barilari, Luca Rizzi, “Sub-Riemannian curvature in contact geometry”, J. Geom. Anal., 27:1 (2017), 366–408 , arXiv: 1505.04374  mathnet  crossref  mathscinet  isi (cited: 12)  scopus (cited: 15)
13. Andrei A. Agrachev, Carolina Biolo, “Switching in Time-Optimal Problem: the 3D Case with 2D Control”, J. Dyn. Control Syst., 23:3 (2017), 577–595 , arXiv: 1605.05232  mathnet  crossref  mathscinet  isi (cited: 2)  elib  scopus (cited: 3)
14. Andrey A. Agrachev, I. Yu. Beschastnyi, “Symplectic geometry of constrained optimization”, Regul. Chaotic Dyn., 22:6 (2017), 750–770  mathnet  crossref  mathscinet  isi  scopus (cited: 1)
15. Andrei A. Agrachev, Francesco Boarotto, Antonio Lerario, “Homotopically invisible singular curves”, Calc. Var. Partial Differential Equations, 56 (2017), 105 , 34 pp.  mathnet  crossref  mathscinet  isi (cited: 1)  scopus (cited: 2)
16. Andrei Agrachev, Ugo Boscain, Jean-Paul Gauthier, Mario Sigalotti, “A note on time-zero controllability and density of orbits for quantum systems”, Proceed. 56th IEEE Conference on Decision and Control, Melbourne, Australia, December 2017, IEEE Conf. Decis. Control, 56, 2017, 5535–5538  mathnet (cited: 1)  crossref  isi  scopus (cited: 1)
17. A. A. Agrachev, R. V. Gamkrelidze, E. S. Golod, A. B. Zhizhchenko, Yu. I. Zhuravlev, V. V. Kozlov, A. V. Mikhalev, A. V. Ovchinnikov, N. Kh. Rozov, A. L. Semenov, V. G. Chirskii, V. A. Shamolin, “Anniversary of Professor M. V. Shamolin”, Dynamical systems, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 134, VINITI, Moscow, 2017, 3–5  mathnet  mathscinet

18. A. A. Agrachev, “Tangent hyperplanes to subriemannian balls”, J. Dyn. Control Syst., 22:4 (2016), 683–692  mathnet  crossref  mathscinet  isi (cited: 2)  elib  scopus (cited: 2)
19. Andrei Agrachev, Yuliy Baryshnikov, Andrey Sarychev, “Ensemble controllability by Lie algebraic methods”, ESAIM: COCV, 22:4 (2016), 921–938 , arXiv: 1603.07133  mathnet  crossref  mathscinet  isi (cited: 7)  scopus (cited: 7)
20. Andrei Agrachev, Davide Barilari, Ugo Boscain, “Introduction to geodesics in sub-Riemannian geometry”, Geometry, Analysis and Dynamics on sub-Riemannian manifolds, v. II, EMS Ser. Lect. Math., Eur. Math. Soc., Zürich, Switzerland, 2016, 1–83  mathnet  crossref
21. A. A. Agrachev, “Topics in sub-Riemannian geometry”, Russian Math. Surveys, 71:6 (2016), 989–1019  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 4)  elib  elib  scopus (cited: 4)

22. Andrei Agrachev, Luca Rizzi, Pavel Silveira, “On conjugate times of LQ optimal control problems”, J. Dyn. Control Syst., 21:4 (2015), 625–641  mathnet  crossref  mathscinet  isi (cited: 5)  elib (cited: 2)  scopus (cited: 8)
23. A. A. Agrachev, “Quadratic cohomology”, Arnold Math. J., 1:1 (2015), 37–58 , arXiv: 1301.2059  mathnet  crossref  mathscinet  zmath  elib  scopus (cited: 1)
24. A. Agrachev, P. W. Y. Lee, “Bishop and Laplacian comparison theorems on three-dimensional contact sub-Riemannian manifolds with symmetry”, J. Geom. Anal., 25 (2015), 512–535  mathnet (cited: 1)  crossref  mathscinet  zmath  isi (cited: 9)  elib  scopus
25. A. A. Agrachev, A. Gentile, A. Lerario, “Geodesics and horizontal-path spaces in Carnot Groups”, Geom. Topol., 19:3 (2015), 1569–1630  mathnet  crossref  mathscinet  zmath  isi (cited: 7)  scopus (cited: 8)

26. A. A. Agrachev, P. Lee, “Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds”, Math. Ann., 360:1-2 (2014), 209–253  mathnet  crossref  mathscinet  zmath  isi (cited: 23)  elib (cited: 4)  scopus (cited: 21)
27. A. Agrachev, “Some open problems”, Geometric Control Theory and Sub-Riemannian Geometry, Springer INDAM Series, 5, 2014, 1–13  crossref  mathscinet  zmath  elib  scopus (cited: 14)

28. A. A. Agrachëv, D. V. Anosov, S. M. Aseev, V. M. Buchstaber, A. M. Vershik, Ya. B. Vorobets, V. A. Kaimanovich, B. S. Kashin, I. G. Lysënok, A. Yu. Ol'shanskii, V. N. Remeslennikov, Ya. G. Sinai, S. K. Smirnov, A. M. Stepin, I. A. Taimanov, E. V. Shchepin, “Rostislav Ivanovich Grigorchuk (on his sixtieth birthday)”, Russian Math. Surveys, 68:5 (2013), 967–971  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib

29. A. Agrachev, D. Barilari, U. Boscain, “On the Hausdorff volume in sub-Riemannian geometry”, Calc. Var. Partial Differential Equations, 43 (2012), 355–388  mathnet  crossref  mathscinet  zmath  isi (cited: 36)  elib (cited: 16)  scopus (cited: 37)
30. A. Agrachev, D. Barilari, “Sub-Riemannian structures in 3D Lie groups”, J. Dyn. Control Syst., 18 (2012), 21–44  mathnet  crossref  mathscinet  zmath  isi (cited: 48)  elib (cited: 29)  scopus (cited: 49)
31. A. A. Agrachev, Yu. Baryshnikov, D. Liberzon, “On robust Lie-algebraic stability conditions for switched linear systems”, Systems Control Lett., 61 (2012), 347–353  mathnet  crossref  mathscinet  zmath  isi (cited: 21)  elib (cited: 3)  scopus (cited: 22)
32. A. Agrachev, L. Lerario, “Systems of quadratic inequalities”, Proc. Lond. Math. Soc. (3), 105:3 (2012), 622–660  mathnet  crossref  mathscinet  zmath  isi (cited: 10)  scopus (cited: 15)
33. A. Agrachev, D. Barilari, U. Boscain, Introduction to Riemannian and sub-Riemannian geometry,, SISSA, Triest, Italiya, 2012 , 179 pp.  mathscinet
34. A. A. Agrachev, D. V. Anosov, I. A. Bogaevskii, A. S. Bortakovskii, A. B. Budak, V. A. Vassiliev, V. V. Goryunov, S. M. Gusein-Zade, A. A. Davydov, V. R. Zarodov, V. D. Sedykh, D. V. Treshchev, V. N. Chubarikov, “Vladimir Mikhailovich Zakalyukin (obituary)”, Russian Math. Surveys, 67:2 (2012), 375–379  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib

35. A. A. Agrachev, R. V. Gamkrelidze, “The geometry of maximum principle”, Proc. Steklov Inst. Math., 273 (2011), 1–22  mathnet  crossref  mathscinet  zmath  isi (cited: 3)  elib
36. A. A. Agrachev, “On the space of symmetric operators with multiple ground states”, Funct. Anal. Appl., 45:4 (2011), 241–251  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 4)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 4)

37. A. A. Agrachev, “Well-posed infinite horizon variational problems on a compact manifold”, Proc. Steklov Inst. Math., 268 (2010), 17–31  mathnet  crossref  mathscinet  zmath  zmath  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
38. A. A. Agrachev, “Invariant Lagrangian submanifolds of dissipative systems”, Russian Math. Surveys, 65:5 (2010), 977–978  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  adsnasa  isi  elib  elib  scopus (cited: 1)
39. A. Agrachev, P. W. Y. Lee, “Continuity of optimal control costs and its application to weak KAM theory”, Calc. Var. Partial Differential Equations, 39:1-2 (2010), 213–232  crossref  mathscinet  zmath  isi (cited: 5)  elib (cited: 3)  scopus (cited: 5)
40. A. A. Agrachev, M. Caponigro, “Dynamics control by a time-varying feedback”, J. Dyn. Control Syst., 16:2 (2010), 149–162  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 2)
41. A. A. Agrachev, U. Boscain, G. Charlot, R. Ghezzi, M. Sigalotti, “Two-dimensional almost-Riemannian structures with tangency points”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 27:3 (2010), 793–807  crossref  mathscinet  zmath  adsnasa  isi (cited: 18)  scopus (cited: 19)
42. 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, “In memory of Evgenii Frolovich Mishchenko”, Proc. Steklov Inst. Math., 271 (2010), 1–2  mathnet  crossref  mathscinet  isi  elib

43. A. A. Agrachev, F. C. Chittaro, “Smooth optimal synthesis for infinite horizon variational problems”, ESAIM Control Optim. Calc. Var., 15:1 (2009), 173–188  crossref  mathscinet  isi (cited: 1)  elib (cited: 1)  scopus (cited: 1)
44. A. Agrachev, U. Boscain, J.-P. Gauthier, F. Rossi, “The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups”, J. Func. Anal., 256:8 (2009), 2621–2655  crossref  mathscinet  zmath  isi (cited: 71)  scopus (cited: 73)
45. A. A. Agrachev, “Any sub-Riemannian metric has points of smoothness”, Russian Math. Dokl., 79:1 (2009), 1–3  mathnet  crossref  mathscinet  zmath  isi (cited: 8)  isi (cited: 8)  elib  scopus (cited: 2)
46. A. Agrachev, P. Lee, “Optimal transportation under nonholonomic constraints”, Trans. Amer. Math. Soc., 361:11 (2009), 6019–6047  crossref  mathscinet  zmath  isi (cited: 24)  elib (cited: 13)  scopus (cited: 26)
47. A. A. Agrachev, M. Caponigro, “Controllability on the group of diffeomorphisms”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26:6 (2009), 2503–2509  crossref  mathscinet  zmath  isi (cited: 10)  elib (cited: 8)  scopus (cited: 12)

48. A. A. Agrachev, F. C. Chittaro, “Extremals flows and infinite horizon optimization”, Mathematical control theory and finance, Springer, Berlin, 2008, 1–13  crossref  mathscinet  zmath  isi (cited: 2)  scopus
49. A. Agrachev, “Hamiltonian systems and optimal control”, Hamiltonian dynamical systems and applications, NATO Sci. Peace Secur. Ser. B Phys. Biophys., Springer, Dordrecht, 2008, 143–156  crossref  mathscinet  zmath  isi  elib  scopus
50. A. Agrachev, A. Sarychev, “Solid controllability in fluid dynamics”, Instability in models connected with fluid flows. I, Int. Math. Ser. (N. Y.), 6, Springer, New York, 2008, 1–35  crossref  mathscinet  zmath
51. A. A. Agrachev, “Geometry of optimal control problems and Hamiltonian systems”, Nonlinear and optimal control theory, Lectures given at the C.I.M.E. Summer School (Cetraro, June 19–29, 2004), Lecture Notes in Math., 1932, eds. P. Nistri, G. Stefani, Springer, Berlin, 2008, 1–59  crossref  mathscinet  mathscinet  zmath  isi (cited: 18)  elib (cited: 8)  scopus (cited: 17)
52. A. Agrachev, U. Boscain, M. Sigalotti, “A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds”, Discrete Contin. Dyn. Syst., 20:4 (2008), 801–822  crossref  mathscinet  zmath  isi (cited: 34)  elib  scopus (cited: 36)
53. A. Agrachev, Any sub-Riemannian Metric has Points of Smoothness, 2008 , arXiv: 0808.4059  adsnasa
54. A. Agrachev, M. Caponigro, Families of vector fields which generate the group of diffeomorphisms, 2008 , arXiv: 0804.4403  adsnasa

55. Agrachev A. A., Boscain U., Sigalotti M., “Two-dimensional almost-Riemannian manifolds”, Subelliptic PDE's and applications to geometry and finance, Lect. Notes Semin. Interdiscip. Mat., 6, Semin. Interdiscip. Mat. (S.I.M.), Potenza, 2007, 17–31  mathscinet  zmath
56. Agrachev A., Zelenko I., “On feedback classification of control-affine systems with one- and two-dimensional inputs”, SIAM J. Control Optim., 46:4 (2007), 1431–1460 (electronic)  crossref  mathscinet  zmath  isi (cited: 11)  elib (cited: 6)  scopus (cited: 10)
57. Agrachev A., Kuksin S., Sarychev A., Shirikyan A., “On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations”, Ann. Inst. H. Poincaré Probab. Statist., 43:4 (2007), 399–415  crossref  mathscinet  zmath  adsnasa  isi (cited: 16)  elib (cited: 11)  scopus (cited: 17)
58. A. A. Agrachev, “Rolling Balls and Octonions”, Proc. Steklov Inst. Math., 258 (2007), 13–22  mathnet  crossref  mathscinet  zmath  elib (cited: 13)  elib (cited: 13)  scopus (cited: 18)
59. A. A. Agrachev, “The Curvature and Hyperbolicity of Hamiltonian Systems”, Proc. Steklov Inst. Math., 256 (2007), 26–46  mathnet  crossref  mathscinet  zmath  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)
60. A. Agrachev, “Optimal control of measures”, Bull. Georgian Natl. Acad. Sci. (N.S.), 1(175):4 (2007), 5–11  mathscinet

61. Agrachev A. A., Sarychev A. V., “Controllability of 2D Euler and Navier-Stokes equations by degenerate forcing”, Comm. Math. Phys., 265:3 (2006), 673–697  crossref  mathscinet  zmath  adsnasa  isi (cited: 20)  elib (cited: 14)  scopus (cited: 19)
62. Agrachev A., Chambrion Th., “An estimation of the controllability time for single-input systems on compact Lie groups”, ESAIM Control Optim. Calc. Var., 12:3 (2006), 409–441 (electronic)  crossref  mathscinet  zmath  isi (cited: 14)  scopus (cited: 16)
63. 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

64. Agrachev A., Marigo A., “Rigid Carnot algebras: a classification”, J. Dyn. Control Syst., 11:4 (2005), 449–494  crossref  mathscinet  zmath  isi (cited: 9)  elib (cited: 5)  scopus (cited: 10)
65. Agrachëv A. A., Shcherbakova N. N., “Hyperbolicity of Hamiltonian systems of negative curvature”, Dokl. Akad. Nauk, 400:3 (2005), 295–298  mathnet (cited: 1)  mathscinet  scopus (cited: 6)
66. Agrachev A. A., Chtcherbakova N. N., Zelenko I., “On curvatures and focal points of dynamical Lagrangian distributions and their reductions by first integrals”, J. Dyn. Control Syst., 11:3 (2005), 297–327  crossref  mathscinet  zmath  isi (cited: 7)  elib (cited: 7)  scopus (cited: 7)
67. Agrachev A. A., Sarychev A. V., “Navier-Stokes equations: controllability by means of low modes forcing”, J. Math. Fluid Mech., 7:1 (2005), 108–152  crossref  mathscinet  zmath  isi (cited: 41)  elib (cited: 31)  scopus (cited: 40)

68. Agrachev A. A., Gamkrelidze R. V., “Vector fields on $n$-foliated $2n$-dimensional manifolds”, J. Math. Sci. (N. Y.), 135:4 (2006), 3093–3108  crossref  mathscinet  zmath  elib  scopus

69. Agrachëv A. A., Sarychev A. V., “Controllability for the Navier-Stokes equation with small control”, Dokl. Akad. Nauk, 394:6 (2004), 727–730  mathnet  mathscinet  zmath  scopus (cited: 2)
70. Agrachev A. A., Sachkov Yu. L., Control theory from the geometric viewpoint, Control Theory and Optimization, II, Encyclopaedia of Mathematical Sciences, 87, Springer-Verlag, Berlin, 2004 , xiv+412 pp.  crossref  mathscinet  zmath

71. Agrachev A., Marigo A., “Nonholonomic tangent spaces: intrinsic construction and rigid dimensions”, Electron. Res. Announc. Amer. Math. Soc., 9 (2003), 111–120 (electronic)  crossref  mathscinet  zmath  isi (cited: 17)  elib (cited: 16)  scopus (cited: 16)
72. Agrachev A. A., Sigalotti M., “On the local structure of optimal trajectories in $\mathbf R^3$”, SIAM J. Control Optim., 42:2 (2003), 513–531 (electronic)  crossref  mathscinet  zmath  isi (cited: 25)  elib (cited: 20)  scopus (cited: 27)

73. Agrachev A. A., “Introduction to optimal control theory”, Mathematical control theory, Part 1, 2 (Trieste, 2001), ICTP Lect. Notes, VIII, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2002, 453–513 (electronic)  mathscinet
74. Agrachev A. A., Stefani G., Zezza P., “Strong optimality for a bang-bang trajectory”, SIAM J. Control Optim., 41:4 (2002), 991–1014 (electronic)  crossref  mathscinet  zmath  isi (cited: 75)  scopus (cited: 80)
75. Agrachev A., Zelenko I., “Geometry of Jacobi curves. II”, J. Dynam. Control Systems, 8:2 (2002), 167–215  crossref  mathscinet  zmath  isi (cited: 21)  elib (cited: 10)  scopus (cited: 16)
76. Agrachev A. A., Stefani G., Zezza P., “Symplectic methods for strong local optimality in the bang-bang case”, Contemporary trends in nonlinear geometric control theory and its applications (México City, 2000), World Sci. Publ., River Edge, NJ, 2002, 169–181  crossref  mathscinet  zmath
77. Agrachev A. A., Zelenko I., “Geometry of Jacobi curves. I”, J. Dynam. Control Systems, 8:1 (2002), 93–140  crossref  mathscinet  zmath  isi (cited: 35)  elib (cited: 27)  scopus (cited: 39)

78. Agrachëv A. A., “A “Gauss-Bonnet formula” for contact sub-Riemannian manifolds”, Dokl. Akad. Nauk, 381:5 (2001), 583–585  mathnet  mathscinet  zmath
79. Agrachev A. A., Liberzon D., “Lie-algebraic stability criteria for switched systems”, SIAM J. Control Optim., 40:1 (2001), 253–269 (electronic)  crossref  mathscinet  zmath  isi (cited: 231)  scopus (cited: 268)
80. Agrachev A., Gauthier J.-P., “On the subanalyticity of Carnot-Caratheodory distances”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 18:3 (2001), 359–382  crossref  mathscinet  zmath  adsnasa  isi (cited: 24)  elib (cited: 24)  scopus (cited: 32)
81. Agrachev A., Zelenko I., “Principal invariants of Jacobi curves”, Nonlinear control in the year 2000 (Paris), Vol. 1, Lecture Notes in Control and Inform. Sci., 258, Springer, London, 2001, 9–21  crossref  mathscinet  zmath
82. Agrachev A., Gauthier J.-P., “Subanalyticity of distance and spheres in sub-Riemannian geometry”, Nonlinear control in the year 2000 (Paris), Vol. 1, Lecture Notes in Control and Inform. Sci., 258, Springer, London, 2001, 1–8  crossref  mathscinet  zmath

83. Agrachev A. A., Charlot G., Gauthier J. P. A., Zakalyukin V. M., “On sub-Riemannian caustics and wave fronts for contact distributions in the three-space”, J. Dynam. Control Systems, 6:3 (2000), 365–395  crossref  mathscinet  zmath  elib (cited: 6)  scopus (cited: 11)
84. Agrachev A. A., Charlot G., Gauthier J.-P. A., Zakalyukin V. M., “On stability of generic subriemannian caustic in the three-space”, C. R. Acad. Sci. Paris Sér. I Math., 330:6 (2000), 465–470  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib (cited: 1)  scopus (cited: 1)

85. Agrachev A. A., “Is it possible to recognize local controllability in a finite number of differentiations?”, Open problems in mathematical systems and control theory, Comm. Control Engrg. Ser., Springer, London, 1999, 15–18  crossref  mathscinet
86. Agrachev A. A., Gauthier J.-P. A., “On the Dido problem and plane isoperimetric problems”, Acta Appl. Math., 57:3 (1999), 287–338  crossref  mathscinet  zmath  isi (cited: 8)  elib (cited: 6)  scopus (cited: 7)
87. Agrachev A. A., Sarychev A. V., “Sub-Riemannian metrics: minimality of abnormal geodesics versus subanalyticity”, ESAIM Control Optim. Calc. Var., 4 (1999), 377–403 (electronic)  crossref  mathscinet  zmath  scopus (cited: 18)
88. Agrachev A., Stefani G., Zezza P., “A Hamiltonian approach to strong minima in optimal control”, Differential geometry and control (Boulder, CO, 1997), Proc. Sympos. Pure Math., 64, Amer. Math. Soc., Providence, RI, 1999, 11–22  crossref  mathscinet  zmath

89. A. A. Agrachev, J.-P. A. Gauthier, “Sub-Riemannian metrics and isoperimetric problems in the contact case”, J. Math. Sci. (New York), 103:6 (2001), 639–663  mathnet  crossref  mathscinet  zmath  elib (cited: 5)  scopus (cited: 8)

90. Agrachev A., “Compactness for sub-Riemannian length-minimizers and subanalyticity”, Control theory and its applications (Grado, 1998), Rend. Sem. Mat. Univ. Politec. Torino, 56, no. 4, 1998, 1–12 (2001)  mathscinet  zmath
91. Agrachev A. A., “Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals”, J. Dynam. Control Systems, 4:4 (1998), 583–604  crossref  mathscinet  zmath  elib (cited: 22)  scopus (cited: 24)
92. Agrachev A., Stefani G., Zezza P., “An invariant second variation in optimal control”, Internat. J. Control, 71:5 (1998), 689–715  crossref  mathscinet  zmath  isi (cited: 18)  elib (cited: 18)  scopus (cited: 23)
93. Agrachev A. A., Chakir El-A. El-H., Gauthier J. P., “Sub-Riemannian metrics on $\mathbf R^3$”, Geometric control and non-holonomic mechanics (Mexico City, 1996), CMS Conf. Proc., 25, Amer. Math. Soc., Providence, RI, 1998, 29–78  mathscinet  zmath
94. Agrachev A., Gamkrelidze R., “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
95. Agrachev A. A., Sarychev A. V., “On abnormal extremals for Lagrange variational problems”, J. Math. Systems Estim. Control, 8:1 (1998), 87–118  mathscinet  scopus (cited: 22)
96. A. A. Agrachev, P. Zezza, G. Stefani, “Strong minima in optimal control”, Proc. Steklov Inst. Math., 220 (1998), 4–22  mathnet  mathscinet  zmath
97. A. A. Agrachev, E. F. Mishchenko, “Introduction. On works of R. V. Gamkrelidze”, Proc. Steklov Inst. Math., 220 (1998), 1–3  mathnet  mathscinet  zmath

98. Agrachev A., Bonnard B., Chyba M., Kupka I., “Sub-Riemannian sphere in Martinet flat case”, ESAIM Control Optim. Calc. Var., 2 (1997), 377–448 (electronic)  crossref  mathscinet  zmath  scopus (cited: 57)
99. Agrachev A. A., Pallaschke D., Scholtes S., “On Morse theory for piecewise smooth functions”, J. Dynam. Control Systems, 3:4 (1997), 449–469  mathscinet  zmath  elib (cited: 18)  scopus (cited: 20)
100. Agrachev A. A., Gamkrelidze R. V., “Feedback-invariant optimal control theory and differential geometry. I. Regular extremals”, J. Dynam. Control Systems, 3:3 (1997), 343–389  crossref  mathscinet  zmath  elib (cited: 41)  scopus (cited: 54)

101. Agrachev A. A., Sarychev A. V., “Abnormal sub-Riemannian geodesics: Morse index and rigidity”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 13:6 (1996), 635–690  crossref  mathscinet  zmath
102. Agrachev A. A., “Exponential mappings for contact sub-Riemannian structures”, J. Dynam. Control Systems, 2:3 (1996), 321–358  crossref  mathscinet  zmath  elib (cited: 43)  scopus (cited: 58)
103. Agrachev Andrei, El Alaoui El-Houcine Chakir, Gauthier Jean-Paul, Kupka Ivan, “Generic singularities of sub-Riemannian metrics on $\mathbf R^3$”, C. R. Acad. Sci. Paris Sér. I Math., 322:4 (1996), 377–384  mathscinet  zmath

104. Agrachev A. A., Sarychev A. V., “On abnormal extremals for Lagrange variational problems”, J. Math. Systems Estim. Control, 5:1 (1995) , 31 pp. (electronic)  mathscinet
105. Agrachev A. A., “Methods of control theory in nonholonomic geometry”, Proceedings of the International Congress of Mathematicians (Zürich, 1994), v. 1, 2, Birkhäuser, Basel, 1995, 1473–1483  crossref  mathscinet  zmath
106. Agrachëv A. A., “On regularity properties of extremal controls”, J. Dynam. Control Systems, 1:3 (1995), 319–324  crossref  mathscinet  zmath  elib (cited: 3)  scopus (cited: 7)
107. Agrachëv A. A., Sarychev A. V., “Strong minimality of abnormal geodesics for 2-distributions”, J. Dynam. Control Systems, 1:2 (1995), 139–176  crossref  mathscinet  zmath  elib (cited: 11)  scopus (cited: 24)
108. 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

109. Agrachëv A. A., Gamkrelidze R. V., “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 (cited: 61)

110. Agrachëv A. A., Gamkrelidze R. V., “Local controllability and semigroups of diffeomorphisms”, Acta Appl. Math., 32:1 (1993), 1–57  crossref  mathscinet  zmath  isi (cited: 15)  elib (cited: 4)  scopus (cited: 18)
111. Agrachëv A. A., Gamkrelidze R. V., “Local controllability for families of diffeomorphisms”, Systems Control Lett., 20:1 (1993), 67–76  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 2)  scopus (cited: 6)

112. Agrachëv A. A., Vakhrameev S. A., “Morse theory and optimal control problems”, Nonlinear synthesis (Sopron, 1989), Progr. Systems Control Theory, 9, Birkhäuser Boston, Boston, MA, 1991, 1–11  mathscinet
113. Agrachëv A. A., “Newton diagrams and tangent cones to attainable sets”, Analysis of controlled dynamical systems (Lyon, 1990), Progr. Systems Control Theory, 8, Birkhäuser Boston, Boston, MA, 1991, 11–20  mathscinet  zmath

114. A. A. Agrachev, R. V. Gamkrelidze, “Volterra series and permutation groups”, J. Math. Sci., 71:3 (1994), 2409–2433  mathnet  crossref  mathscinet  zmath  scopus (cited: 2)

115. E. R. Avakov, A. A. Agrachev, A. V. Arutyunov, “The level set of a smooth mapping in a neighborhood of a singular point, and zeros of a quadratic mapping”, Math. USSR-Sb., 73:2 (1992), 455–466  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 9)  scopus (cited: 8)
116. 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 (cited: 2)  scopus (cited: 2)

117. Soviet Math. Dokl., 41:2 (1990), 227–231 (1991)  mathnet  mathscinet  zmath  isi
118. Agrachëv A. A., Gamkrelidze R. V., “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 (cited: 13)

119. Agrachëv A. A., Gamkrelidze R. V., Sarychev A. V., “Local invariants of smooth control systems”, Acta Appl. Math., 14:3 (1989), 191–237  crossref  mathscinet  zmath  isi (cited: 39)  elib (cited: 24)  scopus (cited: 55)

120. 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 (cited: 10)
121. A. A. Agrachev, R. V. Gamkrelidze, “Quasi-extremality for controllable systems”, J. Soviet Math., 55:4 (1991), 1849–1864  mathnet  crossref  mathscinet  zmath  scopus (cited: 4)
122. 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 (cited: 3)

123. A. A. Agrachev, “One more condition for a conditional extremum”, Russian Math. Surveys, 44:5 (1989), 189–190  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  scopus

124. Soviet Math. Dokl., 37:2 (1988), 493–496  mathnet  mathscinet  zmath  isi
125. Soviet Math. Dokl., 37:2 (1988), 297–300  mathnet  mathscinet  zmath  isi

126. A. A. Agrachev, “The topology of quadratic mappings and Hessians of smooth mappings”, J. Soviet Math., 49:3 (1990), 990–1013  mathnet  crossref  mathscinet  zmath  scopus (cited: 25)
127. A. A. Agrachev, “Quadratic mappings in geometric control theory”, J. Soviet Math., 51:6 (1990), 2667–2734  mathnet  crossref  mathscinet  scopus (cited: 14)

128. Soviet Math. Dokl., 36:1 (1988), 104–108  mathnet  mathscinet  zmath  isi

129. Agrachëv A. A., Gamkrelidze R. V., “Morse and Maslov indices for the extremals of controllable systems”, Dokl. Akad. Nauk SSSR, 287:3 (1986), 521–524  mathnet  mathscinet  zmath  isi (cited: 3)
130. A. A. Agrachev, S. A. Vakhrameev, “Linearly controlled systems of constant rank and relay conditions for extreme control”, Russian Math. Surveys, 41:6 (1986), 199–200  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  scopus (cited: 1)

131. A. A. Agrachev, A. V. Sarychev, “On reduction of a smooth system linear in the control”, Math. USSR-Sb., 58:1 (1987), 15–30  mathnet  crossref  mathscinet  zmath  scopus (cited: 9)

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

133. Agrachëv A. A., Vakhrameev S. A., “Nonlinear control systems of constant rank and bang-bang conditions for extremal controls”, Dokl. Akad. Nauk SSSR, 279:2 (1984), 265–269  mathnet (cited: 1)  mathscinet  isi (cited: 2)

134. Agrachëv A. A., Sarychev A. V., “The control of rotation for an asymmetric rigid body”, Problems Control Inform. Theory/Problemy Upravlen. Teor. Inform., 12:5 (1983), 335–347  mathscinet  zmath

135. 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

136. A. A. Agrachev, S. A. Vakhrameev, “Chronological series and the Cauchy–Kovalevskaya theorem”, J. Soviet Math., 21:2 (1983), 231–250  mathnet  crossref  mathscinet  zmath  scopus

137. 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 (cited: 38)

138. 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 (cited: 26)  scopus (cited: 66)

139. A. A. Agrachev, “A second-order necessary condition for optimality in the general nonlinear case”, Math. USSR-Sb., 31:4 (1977), 493–506  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 4)

140. 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 (cited: 10)  scopus (cited: 14)

141. A. A. Agrachev, “On superpositions of continuous functions”, Math. Notes, 16:4 (1974), 897–900  mathnet  crossref  mathscinet  zmath  scopus

Presentations in Math-Net.Ru
1. Задача быстродействия с управлениями из шара.
A. A. Agrachev
Geometric theory of optimal control
April 1, 2020 16:45
2. Soft construction of Floer-type homologies
A. A. Agrachev
International conference "Classical mechanics, dynamical systems and mathematical physics" on the occasion of Academician Valery V. Kozlov's 70th birthday
January 24, 2020 12:35   
3. Спектр второй вариации
A. A. Agrachev
Geometric theory of optimal control
April 10, 2019
4. Кривизна и долговременное поведение диссипативных систем
A. A. Agrachev
Differential operators on singular spaces, algebraically integrable systems and quantization
April 8, 2019 18:35
5. Homotopically visible and invisible singular trajectories
A. A. Agrachev
International Conference "Optimal Control and Differential Games" dedicated to the 110th anniversary of L. S. Pontryagin
December 12, 2018 12:25   
6. Fast oscillating control
A. A. Agrachev
Colloquium of the Steklov Mathematical Institute of Russian Academy of Sciences
April 5, 2018 16:00   
7. Optimal control and symplectic geometry
A. A. Agrachev
International Conference "Mathematical Theory of Optimal Control" dedicated to the 90th birthday of Academician R. V. Gamkrelidze
June 1, 2017 10:45   
8. Volume geodesic distortion and Ricci curvature for extremals flows
A. A. Agrachev
International Conference "Geometric Analysis and Control Theory"
December 9, 2016 09:30   
9. Geometry and control
A. A. Agrachev
Steklov Mathematical Institute Seminar
May 19, 2016 16:00   
10. Curvature: a variational approach
A. A. Agrachev
Scientific session of the Steklov Mathematical Institute of RAS dedicated to the results of 2015
November 11, 2015 15:30   
11. Экстремали и их оптимальность. Лекция 4
A. A. Agrachev
Summer school "Geometric Control Theory and Analysis on Metric Structures"
July 29, 2014 09:00   
12. Экстремали и их оптимальность. Лекция 3
A. A. Agrachev
Summer school "Geometric Control Theory and Analysis on Metric Structures"
July 28, 2014 10:55   
13. Экстремали и их оптимальность. Лекция 2
A. A. Agrachev
Summer school "Geometric Control Theory and Analysis on Metric Structures"
July 27, 2014 09:00   
14. Экстремали и их оптимальность. Лекция 1
A. A. Agrachev
Summer school "Geometric Control Theory and Analysis on Metric Structures"
July 26, 2014 09:00   
15. Sub-Riemannian curvature
A. A. Agrachev
International Conference "Geometry Days in Novosibirsk, 2013"
August 28, 2013 10:00   
16. О кривизне
A. A. Agrachev
Seminar of the Department of Differential Equations, Steklov Mathematical Institute of RAS
March 27, 2013 12:00
17. Quadratic Cohomology
A. A. Agrachev
International conference "Analysis and Singularities" dedicated to the 75th anniversary of Vladimir Igorevich Arnold
December 21, 2012 10:00   
18. О кривизне гладких задач оптимального управления
A. A. Agrachev
Conference "Differential Equations and Optimal Control", dedicated to the 90th anniversary of E. F. Mishchenko
April 16, 2012 12:10   
19. Системы квадратных уравнений и 16-я проблема Гильберта: приглашение к исследованию
A. A. Agrachev
Homology and homotopy methods in geometry
April 6, 2011 17:00
20. Topology of square-law transformations
A. A. Agrachev
Riemann surfaces, Lie algebras and mathematical physics
April 1, 2011 17:00
21. Неголономная геометрия
Andrei Agrachev
Homology and homotopy methods in geometry
October 13, 2010 17:00
22. Динамика и кривизна
A. A. Agrachev
Meetings of the Moscow Mathematical Society
October 12, 2010 18:30
23. Потоки экстремалей и вариационные задачи с бесконечным горизонтом
A. A. Agrachev
Seminar of the Department of Differential Equations, Steklov Mathematical Institute of RAS
February 25, 2009 12:00
24. Control of diffeomorphisms and densities
A. A. Agrachev
International Conference "Differential Equations and Topology" dedicated to the Centennial Anniversary of L. S. Pontryagin
June 18, 2008 11:20   
25. Векторные распределения и их особые кривые
A. A. Agrachev
Seminar of the Department of Differential Equations, Steklov Mathematical Institute of RAS
April 16, 2008 12:00
26. Nonholonomic geometry
A. A. Agrachev
Meetings of the Moscow Mathematical Society
March 18, 2008
27. Singular curves and invariants of geometric structures
A. A. Agrachev
International conference "Analysis and Singularities" dedicated to 70th anniversary of Vladimir Igorevich Arnold
August 23, 2007 09:00   

Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020