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
Andrei A. Agrachev, Francesco Boarotto, “Normal forms for the endpoint map near nice singular curves for rank-two distributions”, ESAIM: COCV, 27 (2021), S30 , 32 pp. ;
2020
2.
A. Agrachev, D. Barilari, U. Boscain, A comprehensive introduction to sub-Riemannian geometry, Cambridge University Press, 2020 , 763 pp.
3.
Andrei Agrachev, Khazhgali Kozhasov, André Uschmajew, “Chebyshev polynomials and best rank-one approximation ratio”, SIAM J. Matrix Anal. Appl., 41:1 (2020), 308–331;
Andrei Agrachev, Ivan Beschastnyi, “Jacobi fields in optimal control: one-dimensional variations”, J. Dynamical and Control Systems, 26 (2020), 685–732
A. A. Agrachev, “Spectrum of the Second Variation”, Proc. Steklov Inst. Math., 304 (2019), 26–41
7.
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;
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
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
Andrei A. Agrachev, Francesco Boarotto, Antonio Lerario, “Homotopically invisible singular curves”, Calc. Var. Partial Differential Equations, 56 (2017), 105 , 34 pp.
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
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
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
A. A. Agrachev, P. Lee, “Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds”, Math. Ann., 360:1-2 (2014), 209–253
A. Agrachev, D. Barilari, U. Boscain, “On the Hausdorff volume in sub-Riemannian geometry”, Calc. Var. Partial Differential Equations, 43 (2012), 355–388
A. A. Agrachev, Yu. Baryshnikov, D. Liberzon, “On robust Lie-algebraic stability conditions for switched linear systems”, Systems Control Lett., 61 (2012), 347–353
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.
2011
32.
A. A. Agrachev, R. V. Gamkrelidze, “The geometry of maximum principle”, Proc. Steklov Inst. Math., 273 (2011), 1–22
33.
A. A. Agrachev, “On the space of symmetric operators with multiple ground states”, Funct. Anal. Appl., 45:4 (2011), 241–251
2010
34.
A. A. Agrachev, “Well-posed infinite horizon variational problems on a compact manifold”, Proc. Steklov Inst. Math., 268 (2010), 17–31
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
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
A. A. Agrachev, F. C. Chittaro, “Smooth optimal synthesis for infinite horizon variational problems”, ESAIM Control Optim. Calc. Var., 15:1 (2009), 173–188
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
A. A. Agrachev, F. C. Chittaro, “Extremals flows and infinite horizon optimization”, Mathematical control theory and finance, Springer, Berlin, 2008, 1–13
45.
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
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
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
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
A. Agrachev, Any sub-Riemannian Metric has Points of Smoothness, 2008 , arXiv: 0808.4059
50.
A. Agrachev, M. Caponigro, Families of vector fields which generate the group of diffeomorphisms, 2008 , arXiv: 0804.4403
2007
51.
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
52.
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)
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
A. A. Agrachev, “Rolling Balls and Octonions”, Proc. Steklov Inst. Math., 258 (2007), 13–22
55.
A. A. Agrachev, “The Curvature and Hyperbolicity of Hamiltonian Systems”, Proc. Steklov Inst. Math., 256 (2007), 26–46
56.
A. Agrachev, “Optimal control of measures”, Bull. Georgian Natl. Acad. Sci. (N.S.), 1(175):4 (2007), 5–11
2006
57.
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
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)
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
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
65.
Agrachëv A. A., Sarychev A. V., “Controllability for the Navier-Stokes equation with small control”, Dokl. Akad. Nauk, 394:6 (2004), 727–730
66.
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.
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)
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)
70.
Agrachev A. A., Stefani G., Zezza P., “Strong optimality for a bang-bang trajectory”, SIAM J. Control Optim., 41:4 (2002), 991–1014 (electronic)
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
Agrachev A., Gauthier J.-P., “On the subanalyticity of Carnot-Caratheodory distances”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 18:3 (2001), 359–382
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
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
79.
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
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
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
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)
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
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
1998
86.
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)
87.
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
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
90.
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
91.
Agrachev A. A., Sarychev A. V., “On abnormal extremals for Lagrange variational problems”, J. Math. Systems Estim. Control, 8:1 (1998), 87–118
92.
A. A. Agrachev, P. Zezza, G. Stefani, “Strong minima in optimal control”, Proc. Steklov Inst. Math., 220 (1998), 4–22
93.
A. A. Agrachev, E. F. Mishchenko, “Introduction. On works of R. V. Gamkrelidze”, Proc. Steklov Inst. Math., 220 (1998), 1–3
1997
94.
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)
Agrachev A. A., Pallaschke D., Scholtes S., “On Morse theory for piecewise smooth functions”, J. Dynam. Control Systems, 3:4 (1997), 449–469
96.
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
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
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
100.
Agrachev A. A., Sarychev A. V., “On abnormal extremals for Lagrange variational problems”, J. Math. Systems Estim. Control, 5:1 (1995) , 31 pp. (electronic)
101.
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
A. A. Agrachev, R. V. Gamkrelidze, “On the orbits of groups of diffeomorphisms and flows”, Proc. Steklov Inst. Math., 209 (1995), 1–10
1994
105.
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
1993
106.
Agrachëv A. A., Gamkrelidze R. V., “Local controllability and semigroups of diffeomorphisms”, Acta Appl. Math., 32:1 (1993), 1–57
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
109.
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
110.
A. A. Agrachev, R. V. Gamkrelidze, “Volterra series and permutation groups”, J. Math. Sci., 71:3 (1994), 2409–2433
1992
111.
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
112.
A. A. Agrachev, R. V. Gamkrelidze, “Symplectic geometry and conditions necessary conditions for optimality”, Math. USSR-Sb., 72:1 (1992), 29–45
1990
113.
Soviet Math. Dokl., 41:2 (1990), 227–231 (1991)
114.
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
1989
115.
Agrachëv A. A., Gamkrelidze R. V., Sarychev A. V., “Local invariants of smooth control systems”, Acta Appl. Math., 14:3 (1989), 191–237
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
117.
A. A. Agrachev, R. V. Gamkrelidze, “Quasi-extremality for controllable systems”, J. Soviet Math., 55:4 (1991), 1849–1864
118.
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
1989
119.
A. A. Agrachev, “One more condition for a conditional extremum”, Russian Math. Surveys, 44:5 (1989), 189–190
1988
120.
Soviet Math. Dokl., 37:2 (1988), 493–496
121.
Soviet Math. Dokl., 37:2 (1988), 297–300
1990
122.
A. A. Agrachev, “The topology of quadratic mappings and Hessians of smooth mappings”, J. Soviet Math., 49:3 (1990), 990–1013
123.
A. A. Agrachev, “Quadratic mappings in geometric control theory”, J. Soviet Math., 51:6 (1990), 2667–2734
1988
124.
Soviet Math. Dokl., 36:1 (1988), 104–108
1986
125.
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
126.
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
1987
127.
A. A. Agrachev, A. V. Sarychev, “On reduction of a smooth system linear in the control”, Math. USSR-Sb., 58:1 (1987), 15–30
1985
128.
Agrachëv A. A., Gamkrelidze R. V., “The index of extremality and quasiextremal controls”, Dokl. Akad. Nauk SSSR, 284:4 (1985), 777–781
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
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
131.
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
132.
A. A. Agrachev, S. A. Vakhrameev, “Chronological series and the Cauchy–Kovalevskaya theorem”, J. Soviet Math., 21:2 (1983), 231–250
1981
133.
A. A. Agrachev, R. V. Gamkrelidze, “Chronological algebras and nonstationary vector fields”, J. Soviet Math., 17:1 (1981), 1650–1675
1979
134.
A. A. Agrachev, R. V. Gamkrelidze, “The exponential representation of flows and the chronological calculus”, Math. USSR-Sb., 35:6 (1979), 727–785
1977
135.
A. A. Agrachev, “A second-order necessary condition for optimality in the general nonlinear case”, Math. USSR-Sb., 31:4 (1977), 493–506
1976
136.
A. A. Agrachev, R. V. Gamkrelidze, “A second order optimality principle for a time-optimal problem”, Math. USSR-Sb., 29:4 (1976), 547–576
1974
137.
A. A. Agrachev, “On superpositions of continuous functions”, Math. Notes, 16:4 (1974), 897–900
Presentations in Math-Net.Ru
1.
Asymptotic homology in sub-Riemannian geometry A. A. Agrachev International Conference “Differential Equations and Optimal Control” dedicated to the centenary of the birth of Academician Evgenii Frolovich Mishchenko June 7, 2022 12:35
2.
Dynamic planimetrics A. A. Agrachev Seminar "Optimal Control and Dynamical Systems" October 22, 2021 13:00
Soft construction of Floer-type homologies A. A. Agrachev International Conference "Classical Mechanics, Dynamical Systems and Mathematical Physics" on the occasion of V. V. Kozlov 70th birthday January 24, 2020 12:35
8.
Спектр второй вариации A. A. Agrachev Geometric Theory of Optimal Control April 10, 2019
Fast oscillating control A. A. Agrachev Colloquium of Steklov Mathematical Institute of Russian Academy of Sciences April 5, 2018 16:00
12.
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
15.
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
21.
О кривизне A. A. Agrachev Seminar "Optimal Control and Dynamical Systems" March 27, 2013 12:00
22.
Quadratic Cohomology A. A. Agrachev International conference "Analysis and Singularities" dedicated to the 75th anniversary of Vladimir Igorevich Arnold December 21, 2012 10:00
23.
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
Optimal Control and Dynamical Systems, Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze, Trudy Mat. Inst. Steklova, 321, ed. A. A. Agrachev, L. V. Lokutsievskiy, A. V. Sarychev, Yu. L. Sachkov, 2023, 292 с. http://mi.mathnet.ru/book1935
2021
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