Selected Papers of A. AGRACHEV:
1. On superpositions of continuous functions. Matem. zametki,
1974, v.16, 517--522
2. A second order optimality principle for time-optimal
problems. Matem. sbornik, 1976, v.100, 610--643
(with R. Gamkrelidze)
3. A second order necessary condition for optimality in the
general nonlinear case. Matem. sbornik, 1977, V.102
551--568
4. The exponential representation of flows and the chronological
calculus. Matem. sbornik, 1978, v.107, 467--532
(with R. Gamkrelidze)
5 The chronological algebras and nonstationary vector fields.
Itogi nauki. VINITI. Problemy geometrii, 1980, v.11, 135--176
(with R. Gamkrelidze)
6. Chronological series and Cauchy -- Kovalevska theorem.
Itogi nauki. VINITI. Problemy geometrii, 1981, v.12, 165--183
(with S. Vakhrameev)
7. Nonlinear control systems of constant rank and bang-bang
conditions for extremal controls. Dokl. Acad. Nauk SSSR,
1984, v.279, 265--269 (with S. Vakhrameev)
8. The extremality index and quasi-extremal controls. Dokl.
Acad. Nauk SSSR, 1985, v.284, 777--781 (with R. Gamkrelidze)
9. The Morse index and the Maslov index for smooth control
systems. Dokl. Acad. Nauk SSSR, 1986, v.287, 521--524
(with R. Gamkrelidze)
10. On reductions of smooth systems, linear in the control. Matem.
sbornik, 1986, v.130, 18--34 (with A. Sarychev)
11. Filtrations of a Lie algebra of vector fields and nilpotent
approximation of controlled systems. Dokl. Acad.
Nauk SSSR, 1987, v.295, 777--781 (with A. Sarychev)
12. Computation of the Euler characteristic of intersections of
real quadrics. Dokl. Acad. Nauk SSSR, 1988, v.299,
297--300 (with R. Gamkrelidze)
13. Homology of intersections of real quadrics. Dokl. Acad. Nauk
SSSR, 1988, v.299, 493--496
14. Quadratic mappings in the geometric control theory. Itogi nauki.\linebreak
VINITI. Problemy geometrii, 1988, v.20, 111--205
15. Topology of quadratic mappings and Hessians of smooth mappings.
Itogi nauki. VINITI. Algebra. Topologiya. Geometriya,
1988, v.26, 85--124
16. Local invariants of smooth control systems. Acta Appl. Math.,
1989, v.14, 191--237 (with R. Gamkrelidze, A. Sarychev)
17. Ordinary differential equations on vector bundles and the chronological
calculus. Itogi nauki. VINITI. Sovremennye
problemy matematiki. Novejshie dostigeniya,
1989, v.35, 3--107 (with R. Gamkrelidze, S. Vakhrameev)
18. The quasi-extremality for controlled systems. Itogi nauki. VINITI.
Sovremennye problemy matematiki. Novejshie
dostigeniya, 1989, v.35, 109--134 (with R.
Gamkrelidze)
19. Quadratic mappings and smooth vector functions: the Euler characteristics
of the level surfaces. Itogi nauki.
VINITI. Sovremennye problemy matematiki. Novejshie
dostigeniya, 1989, v.35, 179--234 (with R. Gamkrelidze)
20. One more condition for a conditional extremum. Uspekhi Matem.
Nauk, 1989, v.44, 189--190
21. Symplectic geometry for optimal control. In the book: Nonlinear
Controllability and Optimal Control. H.~Sussmann, Ed.
Marcel Dekker, 1990, 263--277 (with R. Gamkrelidze)
22. Symplectic geometry and necessary conditions for optimality.
Matem. sbornik, 1991, v.144, 29--45 (with R. Gamkrelidze)
23. Volterra series and groups of permutations. Itogi nauki. VINITI.
Sovremennye problemy matematiki. Novejshie
dostideniya, 1991, v.39, 3--40 (with R. Gamkrelidze)
24. Morse theory and optimal control problems. In the book: Nonlinear
Synthesis. C.~I.~Byrnes, A.~Kurzhansky, Ed. Proc. Int.
Conf. Sopron, Hungary, 5-9 June, 1989. Birkhauser,
1991, 1--11 (with S. Vakhrameev)
25. Newton diagrams and tangent cones to attainable sets. In the
book: Analysis of Controlled Dynamical Systems.
B. Bonnard, B. Bride, J. P. Gauthier, I. Kupka,
Eds. Proc. col. Int. Lyon, France, 3-6 juillet, 1990. Birkhauser, 1991,
11--20
26. Local controllability for families of diffeomorphisms. Systems
and Control Letters, 1993, v.20, 67--76
(with R. Gamkrelidze)
27. Local controllability and semigroups of diffeomorphisms. Acta
Appl. Math., 1993, v.32, 1--57 (with R. Gamkrelidze)
28. Shuffle products and symmetric groups. In the book: Differential
Equations, Dynamical Systems, and Control
Science. A Festchrift in Honor of Laurence
Markus. Marcel Dekker, 1994, 365--382 (with R. Gamkrelidze)
29. On abnormal extremals for Lagrange variational problems. Mathematical
Systems. Estimation and Control, 1995, v.5,
87--118 (with A. Sarychev)
30. Symplectic methods in optimization
and control. In the book: Geometry of Feedback and Optimal Control. B.~Jakubczyk,
W. Respondek, Eds. Marcel Dekker, 1998, 19--77
(with R. Gamkrelidze)
31. Abnormal sub-Riemannian geodesics: Morse
index and rigidity. Annales de l'Institut Henri Poincare - Analyse non
lineaire,
1996, v.13, 635--690 (with A. Sarychev)
32. Strong minimality of abnormal geodesics
for 2-distributions. J. Dynamical and Control Systems, 1995, v.1, 139--176
(with A. Sarychev)
*33. Methods of control theory in nonholonomic
geometry. Proc. ICM-94, Z\"urich. Birkhauser, 1995, 1473--1483
34. On regularity properties of extremal controls.
J. Dynamical and Control Systems, 1995, v.1, 319--324
35. Exponential mappings for contact sub-Riemannian
structures. J. Dynamical and Control Systems, 1996, v.2, 321--358
36. Sub-Riemannian metrics on R^3.
Proc. Canadian Math. Soc., 1998,
v.25, 29--78 (with H. Chakir, J.-P. Gauthier)
37. Sub-Riemannian sphere in Martinet flat case.
J. ESAIM: Control, Optimisation and Calculus of Variations, 1997, v.2,
377--448 (with B. Bonnard, M. Chyba, I. Kupka)
38. Feedback--invariant optimal control theory
and differential geometry, I. Regular extremals.
J. Dynamical and Control Systems, 1997, v.3,
343--389 (with R. Gamkrelidze)
39. On Morse theory for piecewise smooth functions.
J. Dynamical and Control Systems, 1997, v.3, 449--469
(with S. Scholtes, D. Pallaschke)
40. Is it possible to recognize Local Controllability
in a finite number of differentiations? In the book:
Open Problems in Mathematical Systems and Control
Theory. Springer Verlag, London, 1999, 15--18
*41. Feedback--invariant optimal control theory
and differential geometry, II. Jacobi curves for singular extremals.
J. Dynamical and Control Systems, 1998,
v.4, 583--604
42. On the Dido problem and plane isoperimetric problem. Acta Appl.
Math., 1999, v.57, 287--338 (with J.-P. Gauthier)
43. On the equivalence of different types of local
minima in sub-Riemannian problems.
Proc. 37th IEEE Confer. on Decision and Control,
1998
44. Sub-Riemannian metrics: minimality of abnormal geodesics
versus subanalyticity. ESAIM: J. Control, Optimisation,
and Calculus of Variations, 1999, v.4,
377--403 (with A. Sarychev)
45. Sub-Riemannian metrics and isoperimetric problems in the
contact case. Proc. Int. Confer. Pontryagin-90, 1999, v.3,
5--48 (with J.-P. Gauthier)
46. Compactness for sub-Riemannian length-minimizers
and subanalyticity. Rend. Semin. Mat. Torino, 1998, v.56,
1--12
47. Lie--Algebraic conditions for exponential
stability of switched systems. SIAM J. Control and Optimization, 2001,
253--269 (with D. Liberzon)
48. On sub-Riemannian caustics and wave fronts for contact distributions
in the three-space.
J. Dynamical and Control Systems, 2000, v.6,
365--395 (with J.-P. Gauthier, V. Zakalyukin)
49. On subanalyticity of Carnot---Caratheodory distances.
Annales de l'Institut Henri Poincare`
-- Analyse non lineaire, 2001, v.18, 359--382
(with J.-P. Gauthier)
50. Strong optimality of a bang-bang
trajectory. SIAM J. on Control and Optimization, 2002, v.41, 981--1014
(with G. Stefani, P. Zezza)
51. A "Gauss--Bonnet formula" for contact
sub-Riemannian manifolds. Russian Math. Dokl., 2001, v.381, 583--585
52. Geometry of Jacobi curves, I. J.
Dynamical and Control Systems, 2002, v.8, 93--140 (with I. Zelenko)
53. Geometry of Jacobi curves, II. J.
Dynamical and Control Systems, 2002, v.8, 167--215 (with I. Zelenko)
54. On the local structure of optimal
trajectories in R^3. SIAM J. on Control and Optimization, 2003,
v.42, 513--531
(with M. Sigalotti)
*55. Nonholonomic tangent spaces: intrinsic
construction and rigid dimensions. E.R.A. Amer. Math. Soc., 2003, v.9,
111--120
(with A. Marigo)
56. Navier--Stokes equations: controllability
by means of low modes forcing. J. of Mathematical Fluid Mechanics, 2005,
v.7,
108--152 (with A. Sarychev)
*57. Rigid Carnot algebras: classification.
J. Dynamical and Control Systems, 2005, v.11, 449--494 (with A. Marigo)
58. Hamiltonian systems of negative curvature
are hyperbolic. Russian Math. Dokl., 2005, v.400, 295--298
(with N. Chtcherbakova)
59. On curvatures and focal points of dynamical
Lagrangian distributions and their reductions by first integrals. J.
J. Dynamical and Control Systems, 2005, v.11, 297--327 (with
N. Chtcherbakova, I. Zelenko)
60. An estimation of the controllability
time for single-input systems on compact groups. J. ESAIM:COCV, 2006, v.12, 409--441
(with T. Chambrion)
61. On feedback classification of generic
control-affine systems with one and two-dimensional inputs.
SIAM J. on Control and Optimization, 2007, v.48, 1431--1460
(with I. Zelenko)
62. Controllability of 2D Euler and Navier--Stokes equations
by degenerate forcing. Commun. Math. Phys., 2006, v.265, 673--697
(with A. Sarychev)
63. On finite-dimensional projections of distributions
for solutions of randomly forced PDE's. Annales de l'IHP.
Probabilites et statistiques,
2007, v.43, 399--415 (with S. Kuksin, A. Sarychev, A. Shirikyan)
64. The Pontryagin Maximum Principle 50 years later. Proceed.
Steklov. Math. Inst., 2006,
Dynamical Systems: Modeling, Optimization, and Control,
suppl. 1, S4--S12 (with R. Gamkrelidze)
65. The curvature and hyperbolicty of Hamiltonian systems.
Proceed. Steklov Math. Inst., 2007, v.256, 26--46
66. Nurowski's conformal structures for (2,5)-distributions
via dynamics of abnormal extremals. Proceed. RIMS workshop
Developments of Cartan geometry and related mathematical problems;
Kyoto, 2006, 204--218 (with I. Zelenko)
67. A Gauss--Bonnet--like formula on two-dimensional
almost Riemannian manifolds.
Discrete and Continuous Dynamical Systems, 2008, v.20, 801--822
(with U. Boscain, M. Sigalotti)
68. Rolling balls and Octonions.
Proceed. Steklov Math. Inst., 2007, v.258, 13--22
**69. Solid controllability in fluid dynamics.
In the book: Instabilities in Models Connected with Fluid Flow. I.
Springer, 2007, 1--36 (with A. Sarychev)
70. Smooth optimal synthesis for infinite horizon variational problems.
J. ESAIM:COCV, 2009, v.15, 173--188 (with F. Chittaro)
71. Optimal transport under nonholonomic constraints.
Transactions of the Amer. Math. Soc., 2009, v.361, 6019--6047 (with P. Lee)
72. Controllability on the group of diffeomorphisms.
Annales de l'Institut Henri Poincare` -- Analyse non lineaire, 2009, v.26, 2503--2509
(with M. Caponigro)
73. The intrinsic hypoelliptic Laplacian and its heat kernel
on unimodular Lie groups. J. Func. An., 2009, v.256, 2621--2655 (with U. Boscain, J.-P. Gauthier, F. Rossi)
*74. Any sub-Riemannian metric has points of smoothness. Russian Math. Dokl.,
2009, v.79, 1--3
75. Dynamics control by a time-varying feedback. J. Dynamical and Control Systems,
2010, v.16, 149--162 (with M. Caponigro)
76. Generalized Ricci curvature bounds for three dimensional contact
subriemannian manifolds. Math. Ann., 2014, v.360, 209--253 (with P. Lee)
*77. Well-posed infinite horizon variational problems.
Proceed. Steklov Math. Inst., 2010, v.268, 17--31
78. Two-dimensional almost Riemannian structures with tangency points.
Annales de l'Institut Henri Poincare` -- Analyse non lineaire, 2010, v.27, 793--807
(with U. Boscain, G. Charlot, R. Ghezzi, M. Sigalotti)
79. Continuity of optimal control cost and its application to weak
KAM theory. Calculus of Variations and Part. Dif. Eq., 2010, v.39, 213--232 (with P. Lee)
80. Invariant Lagrange submanifolds of dissipative systems.
Russian Math. Surveys, 2010, v.65, 222--223
81. On the Hausdorff volume in sub-Riemannian geometry.
Calculus of Variations and Part. Dif. Eq., 2012, v.43, 355--388 (with D. Barilari, U. Boscain)
82. Sub-Riemanian structures on 3D Lie groups.
J. Dynamical and Control Systems, 2012, v.18, 21--44 (with D. Barilari)
83. On robust Lie-algebraic stability conditions for switched
linear systems. Systems and Control Letters, 2012, v.61, 347--353 (with Yu. Baryshnikov, D. Liberzon)
84. Systems of quadratic inequalities. Proceed. London Math. Soc.,
2012, v.105, 622--660 (with A. Lerario)
85. Bishop and Laplacian comparison theorems on 3D
contact sub-Riemannian manifolds with symmetry. J. Geom. Anal., 2015, v.25, 512--535 (with P. Lee)
86. On the space of symmetric operators with multiple ground states.
Func. Anal. and its Appl., 2011, v.45, 241--251
87. Quadratic cohomology. Arnold Math. J., 2015, v.1, 37--58
88. On conjugate times of LQ optimal control problems.
J. Dynamical and Control Systems, 2015, v.21, 625--641 (with L. Rizzi, P. Silveira)
89. Geodesics and horizontal-path spaces in Carnot groups. Geometry & Topology,
2015, v.19, 1569--1630 (with A. Gentile, A. Lerario)
90. Tangent hyperplanes to subriemannian balls.
J. Dynamical and Control Systems, 2016, v.22, 683--692
91. Sub-Riemannian curvature in contact geometry. J. Geom. Anal., 2017, v.27,
366--408 (with D. Barilari, L. Rizzi)
92. Intrinsic random walks in Riemannian and
sub-Riemannian geometry via volume sampling. J. ESAIM:COCV, 2018, v.24, 1075--1105 (with U. Boscain, R. Neel, L. Rizzi)
93. Volume geodesic distortion and
Ricci curvature for Hamiltonian dynamics. Annals de l'Institut Fourier, 2019, v.69, 1187--1228 (with D. Barilari, E. Paoli)
94. Ensemble controllability by Lie algebraic
methods. J. ESAIM:COCV, 2016, v.22, 921--938 (with Yu. Baryshnikov, A. Sarychev)
95. Homotopically invisible singular curves. Calculus of Variations and Part. Dif. Eq.,
2017, v.56, 1--34 (with F. Boarotto, A. Lerario)
96. Switching in time-optimal problem. The 3-D case with 2-D control.
J. Dynamical and Control Systems, 2017, v.23, 577--595 (with C. Biolo)
97. Switching in time-optimal problem with control in a ball.
SIAM J. on Control and Optimization, 2018, v.56, 183--200 (with C. Biolo)
98. Optimality of broken extremals. J. Dynamical and Control Systems, 2019, v.25, 289--307 (with C. Biolo)
99. Spectrum of the second variation. Proceed. Steklov Math. Inst., 2019, v.304, 26--41
100. Jacobi fields in optimal control: Morse and Maslov indices. Nonlinear Analysis, 2022, v.214, 47p. (with I. Beschastnyi)
101. Structure of the endpoint map near nice singular curves. J. ESAIM:COCV, 2021, v.27, 32p. (with F. Boarotto)
102. Jacobi fields in optimal control: One-dimensional variations. J. Dynamical and Control Systems,
2020, v.26, 685--732 (with I. Beschastnyi)
103. Chebyshev polynomials and best rank-one approximation ratio. SIAM J. Matrix Anal. Appl., 2020, v.41, 308--331
(with K. Kozhasov, A. Uschmajev)
104. Control in the space of ensembles of points. SIAM J. on Control and Optimization, 2020, v.58, 1579--1596
(with A. Sarychev)
105. Control On the manifolds of mappings with a view to the deep learning. J. Dynamical and Control Systems, 2022,
v.28, 989--1008 (with A. Sarychev)
106. Ants and bracket generating distributions in dimensions 5 and 6. Automatica, 2023, v.147, 1--10
(with P. Nurowski)
107. Relative heat content asymptotics for sub-Riemannian manifolds. Analysis & PDE, to appear
(with L. Rizzi, T. Rossi)
108. Index theorems for graph-parametrized optimal control problems. Nonlinearity, 2023, v.36, 2792--2838
(with S. Baranzini, I. Beschastnyi)
109. "Good Lie brackets" for control affine systems. J. Dynamical and Control Systems, 2024, v.30, 18p.
110. Lyapunov exponents of linear switching systems (with M. Motta)
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* Updated after the publication.
** Preliminary version.