Mathematical control theory, sub-Riemannian geometry and and related topics in dynamical systems, geometry and topology.
Main publications:
Agrachev A. A., Gauthier J.-P., “On subanalyticity of Carnot–Caratheodory distances”, Annales de lInst. Henry Poincare – Analyse non lineaire, 18 (2001), 359–382
Agrachev A. A. Sarychev A. V., “Controllability of 2D Euler and Navier–Stokes equations by
degenerate forcing”, Commun. Math. Phys., 265 (2006), 673–697
Agrachev A. A., “Well-posed infinite horizon variational problems on a compact manifold”, Proceed. Steklov Math. Inst., 268 (2010), 24–39
Agrachev A. A., Lerario A., “Systems of quadratic inequalities”, Proceedings of the London Math. Soc., 105 (2012), 622–660
Agrachev A. A., Barilari D., Rizzi L., “Curvature: A variational approach”, Memoirs of the American Math. Soc., 256 (2018), 1–116
A. Agrachev, D. Barilari, U. Boscain, A comprehensive introduction to sub-Riemannian geometry, Cambridge University Press (to appear) , 643 pp.
2019
2.
A. A. Agrachev, “Spectrum of the Second Variation”, Proc. Steklov Inst. Math., 304 (2019), 26–41
2018
3.
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 (cited: 32)
4.
Andrei A. Agrachev, Carolina Biolo, “Switching in time-optimal problem with control in a ball”, SIAM J. Control Optim., 156:1 (2018), 183–200
5.
A. Agrachev, D. Barilari, E. Paoli, “Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics”, Annales de l'Institut Fourier, 2018 (to appear) , arXiv: 1602.08745
6.
A. Agrachev, Spectrum of the second variation, 2018 , 22 pp., arXiv: 1807.10527
7.
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 (cited: 2)
8.
Andrei A. Agrachev, Carolina Biolo, “Optimality of broken extremals”, J. Dyn. Control Syst., 25:2 (2018), 289–307
2017
9.
Andrei Agrachev, Davide Barilari, Luca Rizzi, “Sub-Riemannian curvature in contact geometry”, J. Geom. Anal., 27:1 (2017), 366–408 , arXiv: 1505.04374 (cited: 11) (cited: 14)
10.
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 (cited: 2) (cited: 2)
11.
Andrey A. Agrachev, I. Yu. Beschastnyi, “Symplectic geometry of constrained optimization”, Regul. Chaotic Dyn., 22:6 (2017), 750–770
12.
Andrei A. Agrachev, Francesco Boarotto, Antonio Lerario, “Homotopically invisible singular curves”, Calc. Var. Partial Differential Equations, 56 (2017), 105 , 34 pp. (cited: 1) (cited: 1)
13.
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
14.
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
2016
15.
A. A. Agrachev, “Tangent hyperplanes to subriemannian balls”, J. Dyn. Control Syst., 22:4 (2016), 683–692 (cited: 2) (cited: 2)
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
18.
A. A. Agrachev, “Topics in sub-Riemannian geometry”, Russian Math. Surveys, 71:6 (2016), 989–1019 (cited: 3) (cited: 3)
2015
19.
Andrei Agrachev, Luca Rizzi, Pavel Silveira, “On conjugate times of LQ optimal control problems”, J. Dyn. Control Syst., 21:4 (2015), 625–641 (cited: 4) (cited: 2) (cited: 6)
20.
A. A. Agrachev, “Quadratic cohomology”, Arnold Math. J., 1:1 (2015), 37–58 , arXiv: 1301.2059
21.
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 (cited: 1) (cited: 8)
22.
A. A. Agrachev, A. Gentile, A. Lerario, “Geodesics and horizontal-path spaces in Carnot Groups”, Geom. Topol., 19:3 (2015), 1569–1630 (cited: 7) (cited: 7)
2014
23.
A. A. Agrachev, P. Lee, “Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds”, Math. Ann., 360:1-2 (2014), 209–253 (cited: 22) (cited: 4) (cited: 20)
24.
A. Agrachev, “Some open problems”, Geometric Control Theory and Sub-Riemannian Geometry, Springer INDAM Series, 5, 2014, 1–13
2013
25.
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
2012
26.
A. Agrachev, D. Barilari, U. Boscain, “On the Hausdorff volume in sub-Riemannian geometry”, Calc. Var. Partial Differential Equations, 43 (2012), 355–388 (cited: 36) (cited: 16) (cited: 37)
27.
A. Agrachev, D. Barilari, “Sub-Riemannian structures in 3D Lie groups”, J. Dyn. Control Syst., 18 (2012), 21–44 (cited: 48) (cited: 29) (cited: 49)
28.
A. A. Agrachev, Yu. Baryshnikov, D. Liberzon, “On robust Lie-algebraic stability conditions for switched linear systems”, Systems Control Lett., 61 (2012), 347–353 (cited: 16) (cited: 3) (cited: 16)
29.
A. Agrachev, L. Lerario, “Systems of quadratic inequalities”, Proc. Lond. Math. Soc. (3), 105:3 (2012), 622–660 (cited: 10) (cited: 14)
30.
A. Agrachev, D. Barilari, U. Boscain, Introduction to Riemannian and sub-Riemannian geometry, http://hdl.handle.net/1963/5877, SISSA, Triest, Italiya, 2012 , 179 pp.
31.
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
2011
32.
A. A. Agrachev, R. V. Gamkrelidze, “The geometry of maximum principle”, Proc. Steklov Inst. Math., 273 (2011), 1–22 (cited: 3)
33.
A. A. Agrachev, “On the space of symmetric operators with multiple ground states”, Funct. Anal. Appl., 45:4 (2011), 241–251 (cited: 4) (cited: 2) (cited: 2) (cited: 4)
2010
34.
A. A. Agrachev, “Well-posed infinite horizon variational problems on a compact manifold”, Proc. Steklov Inst. Math., 268 (2010), 17–31 (cited: 1) (cited: 1) (cited: 1) (cited: 1)
35.
A. A. Agrachev, “Invariant Lagrangian submanifolds of dissipative systems”, Russian Math. Surveys, 65:5 (2010), 977–978
36.
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 (cited: 5) (cited: 3) (cited: 5)
37.
A. A. Agrachev, M. Caponigro, “Dynamics control by a time-varying feedback”, J. Dyn. Control Syst., 16:2 (2010), 149–162 (cited: 1) (cited: 2)
38.
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 (cited: 18) (cited: 19)
39.
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
2009
40.
A. A. Agrachev, F. C. Chittaro, “Smooth optimal synthesis for infinite horizon variational problems”, ESAIM Control Optim. Calc. Var., 15:1 (2009), 173–188 (cited: 1) (cited: 1) (cited: 1)
41.
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 (cited: 66) (cited: 70)
42.
A. A. Agrachev, “Any sub-Riemannian metric has points of smoothness”, Russian Math. Dokl., 79:1 (2009), 1–3 (cited: 8) (cited: 8) (cited: 2)
43.
A. Agrachev, P. Lee, “Optimal transportation under nonholonomic constraints”, Trans. Amer. Math. Soc., 361:11 (2009), 6019–6047 (cited: 24) (cited: 13) (cited: 26)
44.
A. A. Agrachev, M. Caponigro, “Controllability on the group of diffeomorphisms”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26:6 (2009), 2503–2509 (cited: 10) (cited: 8) (cited: 12)
2008
45.
A. A. Agrachev, F. C. Chittaro, “Extremals flows and infinite horizon optimization”, Mathematical control theory and finance, Springer, Berlin, 2008, 1–13 (cited: 2)
46.
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
47.
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
48.
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 (cited: 18) (cited: 8) (cited: 17)
49.
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 (cited: 33) (cited: 35)
50.
A. Agrachev, Any sub-Riemannian Metric has Points of Smoothness, 2008 , arXiv: 0808.4059
51.
A. Agrachev, M. Caponigro, Families of vector fields which generate the group of diffeomorphisms, 2008 , arXiv: 0804.4403
2007
52.
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
53.
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) (cited: 11) (cited: 6) (cited: 10)
54.
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 (cited: 15) (cited: 11) (cited: 15)
55.
A. A. Agrachev, “Rolling Balls and Octonions”, Proc. Steklov Inst. Math., 258 (2007), 13–22 (cited: 13) (cited: 13) (cited: 18)
56.
A. A. Agrachev, “The Curvature and Hyperbolicity of Hamiltonian Systems”, Proc. Steklov Inst. Math., 256 (2007), 26–46 (cited: 1) (cited: 1) (cited: 2)
57.
A. Agrachev, “Optimal control of measures”, Bull. Georgian Natl. Acad. Sci. (N.S.), 1(175):4 (2007), 5–11
2006
58.
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 (cited: 18) (cited: 14) (cited: 18)
59.
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) (cited: 14) (cited: 16)
60.
A. A. Agrachev, R. V. Gamkrelidze, “The Pontryagin Maximum Principle 50 years later”, Proc. Inst. Math. Mech., 253, suppl. 1 (2006), S4–S12
2005
61.
Agrachev A., Marigo A., “Rigid Carnot algebras: a classification”, J. Dyn. Control Syst., 11:4 (2005), 449–494 (cited: 9) (cited: 5) (cited: 10)
62.
Agrachëv A. A., Shcherbakova N. N., “Hyperbolicity of Hamiltonian systems of negative curvature”, Dokl. Akad. Nauk, 400:3 (2005), 295–298 (cited: 1) (cited: 6)
63.
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 (cited: 7) (cited: 7) (cited: 7)
64.
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 (cited: 39) (cited: 31) (cited: 38)
2006
65.
Agrachev A. A., Gamkrelidze R. V., “Vector fields on $n$-foliated $2n$-dimensional manifolds”, J. Math. Sci. (N. Y.), 135:4 (2006), 3093–3108
2004
66.
Agrachëv A. A., Sarychev A. V., “Controllability for the Navier-Stokes equation with small control”, Dokl. Akad. Nauk, 394:6 (2004), 727–730 (cited: 2)
67.
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.
2003
68.
Agrachev A., Marigo A., “Nonholonomic tangent spaces: intrinsic construction and rigid dimensions”, Electron. Res. Announc. Amer. Math. Soc., 9 (2003), 111–120 (electronic) (cited: 17) (cited: 16) (cited: 16)
69.
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) (cited: 24) (cited: 20) (cited: 27)
2002
70.
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)
71.
Agrachev A. A., Stefani G., Zezza P., “Strong optimality for a bang-bang trajectory”, SIAM J. Control Optim., 41:4 (2002), 991–1014 (electronic) (cited: 73) (cited: 75)
72.
Agrachev A., Zelenko I., “Geometry of Jacobi curves. II”, J. Dynam. Control Systems, 8:2 (2002), 167–215 (cited: 20) (cited: 10) (cited: 15)
73.
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
74.
Agrachev A. A., Zelenko I., “Geometry of Jacobi curves. I”, J. Dynam. Control Systems, 8:1 (2002), 93–140 (cited: 34) (cited: 27) (cited: 38)
2001
75.
Agrachëv A. A., “A “Gauss-Bonnet formula” for contact sub-Riemannian manifolds”, Dokl. Akad. Nauk, 381:5 (2001), 583–585
76.
Agrachev A. A., Liberzon D., “Lie-algebraic stability criteria for switched systems”, SIAM J. Control Optim., 40:1 (2001), 253–269 (electronic) (cited: 226) (cited: 259)
77.
Agrachev A., Gauthier J.-P., “On the subanalyticity of Carnot-Caratheodory distances”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 18:3 (2001), 359–382 (cited: 22) (cited: 24) (cited: 32)
78.
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
79.
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
2000
80.
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 (cited: 6) (cited: 11)
81.
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 (cited: 2) (cited: 1)
1999
82.
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
83.
Agrachev A. A., Gauthier J.-P. A., “On the Dido problem and plane isoperimetric problems”, Acta Appl. Math., 57:3 (1999), 287–338 (cited: 8) (cited: 6) (cited: 7)
84.
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)
85.
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
2001
86.
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 (cited: 5) (cited: 8)
1998
87.
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)
88.
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 (cited: 22) (cited: 24)
89.
Agrachev A., Stefani G., Zezza P., “An invariant second variation in optimal control”, Internat. J. Control, 71:5 (1998), 689–715 (cited: 18) (cited: 18) (cited: 23)
90.
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
91.
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
92.
Agrachev A. A., Sarychev A. V., “On abnormal extremals for Lagrange variational problems”, J. Math. Systems Estim. Control, 8:1 (1998), 87–118 (cited: 22)
93.
A. A. Agrachev, P. Zezza, G. Stefani, “Strong minima in optimal control”, Proc. Steklov Inst. Math., 220 (1998), 4–22
94.
A. A. Agrachev, E. F. Mishchenko, “Introduction. On works of R. V. Gamkrelidze”, Proc. Steklov Inst. Math., 220 (1998), 1–3
1997
95.
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)
96.
Agrachev A. A., Pallaschke D., Scholtes S., “On Morse theory for piecewise smooth functions”, J. Dynam. Control Systems, 3:4 (1997), 449–469 (cited: 18) (cited: 18)
97.
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 (cited: 41) (cited: 53)
1996
98.
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
99.
Agrachev A. A., “Exponential mappings for contact sub-Riemannian structures”, J. Dynam. Control Systems, 2:3 (1996), 321–358 (cited: 43) (cited: 56)
100.
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
1995
101.
Agrachev A. A., Sarychev A. V., “On abnormal extremals for Lagrange variational problems”, J. Math. Systems Estim. Control, 5:1 (1995) , 31 pp. (electronic)
102.
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
103.
Agrachëv A. A., “On regularity properties of extremal controls”, J. Dynam. Control Systems, 1:3 (1995), 319–324 (cited: 3) (cited: 7)
104.
Agrachëv A. A., Sarychev A. V., “Strong minimality of abnormal geodesics for 2-distributions”, J. Dynam. Control Systems, 1:2 (1995), 139–176 (cited: 11) (cited: 24)
105.
A. A. Agrachev, R. V. Gamkrelidze, “On the orbits of groups of diffeomorphisms and flows”, Proc. Steklov Inst. Math., 209 (1995), 1–10
1994
106.
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 (cited: 61)
1993
107.
Agrachëv A. A., Gamkrelidze R. V., “Local controllability and semigroups of diffeomorphisms”, Acta Appl. Math., 32:1 (1993), 1–57 (cited: 15) (cited: 4) (cited: 18)
108.
Agrachëv A. A., Gamkrelidze R. V., “Local controllability for families of diffeomorphisms”, Systems Control Lett., 20:1 (1993), 67–76 (cited: 3) (cited: 2) (cited: 6)
1991
109.
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
110.
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
1994
111.
A. A. Agrachev, R. V. Gamkrelidze, “Volterra series and permutation groups”, J. Math. Sci., 71:3 (1994), 2409–2433 (cited: 1)
1992
112.
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 (cited: 9) (cited: 8)
113.
A. A. Agrachev, R. V. Gamkrelidze, “Symplectic geometry and conditions necessary conditions for optimality”, Math. USSR-Sb., 72:1 (1992), 29–45 (cited: 2) (cited: 2)
1990
114.
Soviet Math. Dokl., 41:2 (1990), 227–231 (1991)
115.
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 (cited: 13)
1989
116.
Agrachëv A. A., Gamkrelidze R. V., Sarychev A. V., “Local invariants of smooth control systems”, Acta Appl. Math., 14:3 (1989), 191–237 (cited: 38) (cited: 24) (cited: 55)
1991
117.
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 (cited: 10)
118.
A. A. Agrachev, R. V. Gamkrelidze, “Quasi-extremality for controllable systems”, J. Soviet Math., 55:4 (1991), 1849–1864 (cited: 4)
119.
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 (cited: 3)
1989
120.
A. A. Agrachev, “One more condition for a conditional extremum”, Russian Math. Surveys, 44:5 (1989), 189–190 (cited: 2)
1988
121.
Soviet Math. Dokl., 37:2 (1988), 493–496
122.
Soviet Math. Dokl., 37:2 (1988), 297–300
1990
123.
A. A. Agrachev, “The topology of quadratic mappings and Hessians of smooth mappings”, J. Soviet Math., 49:3 (1990), 990–1013 (cited: 25)
124.
A. A. Agrachev, “Quadratic mappings in geometric control theory”, J. Soviet Math., 51:6 (1990), 2667–2734 (cited: 14)
1988
125.
Soviet Math. Dokl., 36:1 (1988), 104–108
1986
126.
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 (cited: 3)
127.
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 (cited: 1) (cited: 1)
1987
128.
A. A. Agrachev, A. V. Sarychev, “On reduction of a smooth system linear in the control”, Math. USSR-Sb., 58:1 (1987), 15–30 (cited: 9)
1985
129.
Agrachëv A. A., Gamkrelidze R. V., “The index of extremality and quasiextremal controls”, Dokl. Akad. Nauk SSSR, 284:4 (1985), 777–781 (cited: 3) (cited: 3)
1984
130.
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 (cited: 1) (cited: 2)
1983
131.
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
1985
132.
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
1983
133.
A. A. Agrachev, S. A. Vakhrameev, “Chronological series and the Cauchy–Kovalevskaya theorem”, J. Soviet Math., 21:2 (1983), 231–250
1981
134.
A. A. Agrachev, R. V. Gamkrelidze, “Chronological algebras and nonstationary vector fields”, J. Soviet Math., 17:1 (1981), 1650–1675 (cited: 36)
1979
135.
A. A. Agrachev, R. V. Gamkrelidze, “The exponential representation of flows and the chronological calculus”, Math. USSR-Sb., 35:6 (1979), 727–785 (cited: 20) (cited: 62)
1977
136.
A. A. Agrachev, “A second-order necessary condition for optimality in the general nonlinear case”, Math. USSR-Sb., 31:4 (1977), 493–506 (cited: 1) (cited: 3)
1976
137.
A. A. Agrachev, R. V. Gamkrelidze, “A second order optimality principle for a time-optimal problem”, Math. USSR-Sb., 29:4 (1976), 547–576 (cited: 10) (cited: 14)
1974
138.
A. A. Agrachev, “On superpositions of continuous functions”, Math. Notes, 16:4 (1974), 897–900
Presentations in Math-Net.Ru
1.
Спектр второй вариации A. A. Agrachev Geometric theory of optimal control April 10, 2019
Fast oscillating control A. A. Agrachev Colloquium of the Steklov Mathematical Institute of Russian Academy of Sciences April 5, 2018 16:00
5.
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
Geometry and control A. A. Agrachev Steklov Mathematical Institute Seminar May 19, 2016 16:00
8.
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
Sub-Riemannian curvature A. A. Agrachev International Conference "Geometry Days in Novosibirsk, 2013" August 28, 2013 10:00
14.
О кривизне A. A. Agrachev Seminar of the Department of Differential Equations, Steklov Mathematical Institute of RAS March 27, 2013 12:00
15.
Quadratic Cohomology A. A. Agrachev International conference "Analysis and Singularities" dedicated to the 75th anniversary of Vladimir Igorevich Arnold December 21, 2012 10:00
16.
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
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
23.
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
24.
Nonholonomic geometry A. A. Agrachev Meetings of the Moscow Mathematical Society March 18, 2008
2019
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