Selected publications and talks of Yuri L. Sachkov


The complete list of publications please see in Curriculum Vitae (PDF file)


(with A. Mashtakov), Superintegrability of Sub-Riemannian Problems on Unimodular 3D Lie Groups, , submitted, arXiv:1405.1716v1 [math.OC] 7 May 2014. (PDF file)


Sub-Riemannian geodesics on the free Carnot group with the growth vector (2,3,5,8), , submitted, arXiv:1404.7752v1 [math.OC] 30 Apr 2014. (PDF file)


(with U. Boscain, R. Duits, F. Rossi) Association fields via cuspless sub-Riemannian geodesics in SE(2), , J Math Imaging Vis, June 2014, Volume 49, Issue 2, pp 384--417. (PDF file)


(with U. Boscain, R. Duits, F. Rossi) Optimal control for reconstruction of curves without cusps, , ESAIM: Control, Optimisation and Calculus of Variations, accepted, \texttt{arXiv:1203.3089v1 [math.OC] 14 Mar 2012} (PDF file)


(with Yasir Awais Butt, Aamer Iqbal Bhatti), Parametrization of Extremal Trajectories in Sub-Riemannian Problem on Group of Motions of Pseudo Euclidean Plane , Journal of Dynamical and Control Systems, Vol. 20 (2014), No. 3 (July), in print. arXiv:submit/0695903 [math.OC] 6 May 2013. (PDF file)


Integrability of free nilpotent sub-Riemannian structure with the growth vector (2,3,5,8), A talk at the seminar of Prof. M.I.Zelikin (Moscow University, April 17 2013) (PDF file)


(with E.Sachkova), Exponential mapping in Euler's elastic problem, Journal of Dynamical and Control Systems, Vol. 20 (2014), in print. arXiv:1303.1746v1 [math.OC] 7 Mar 2013. (PDF file)


(with A.Ardentov), Conjugate points in nilpotent sub-Riemannian problem on the Engel group, Journal of Mathematical Sciences, (2013), to appear. arXiv:1209.2865v1 [math.OC] 13 Sep 2012. (PDF file)


Image inpainting, neurogeometry of vision, and sub-Riemannian geometry, A talk at the seminar of Computer Science department of Moscow State University (November 26 2012) (PDF file)


Low-dimensional left-invariant sub-Riemannian problems, A talk at the conference "Geometric control and sub-Riemannian geometry" dedicated to 60-th birthday of A.A.Agrachev (Cortona, Italy, May 2125 2012) (PDF file, 9 Mb)


Closed Euler elasticae, Proceedings of the Steklov Institute of Mathematics, V. 278 (2012), 218-232 (PDF file)


(with A.Ardentov, A.Mashtakov) Inpainting via sub-Riemannian minimizers on the group of rototranslations, Numer. Math. Theor. Meth. Appl., Vol. 6, No. 1, pp. 95-115. (PDF file)


Sub-Riemannian problem on the group of motions of a plane, A talk at the Control Theory Seminar (University of Rouen, November 18, 2010) (PDF file, 22 Mb)


Stability of Euler elasticae centered at verices or inflection points, Proceedings of the Steklov Institute of Mathematics}, V. 271 (2010), 187--203. (PDF file, 5 Mb)


Symmetries and Maxwell strata in the plate-ball problem, Sbornik: Mathematics, V. 201 (2010), N 7, 1029--1091. (PDF file)


Cut locus in sub-Riemannian problem on the group of motions of a plane, A talk at the International conference on Mathematical Control Theory and Mechanics (Suzdal', July 3 -- 7, 2009) (PDF file, 7 Mb) (rar archive, 3 Mb)


Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane, ESAIM: COCV, 17 (2011), 293--321 (available also at arXiv:0903.0727 [math.OC]) (PDF file)


Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane, ESAIM: COCV, 16 (2010), 1018--1039, (available also at arXiv:0903.0727 [math.OC]) (PDF file)


(with I. Moiseev) Maxwell strata in sub-Riemannian problem on the group of motions of a plane, ESAIM: COCV, 16 (2010), 380--399, (available also at arXiv:0807.4731v1, 29 July 2008). (PDF file)


Euler's elastic problem, A talk in University Milano Bicocca (January 20, 2009) (PDF file)


(with A. Ardentov) Solution of Euler's elastic problem (in Russian), Avtomatika i Telemekhanika, 2009, No. 4. (PDF file) English translation appears in Automation and remote control.


Conjugate points in Euler's elastic problem, Journal of Dynamical and Control Systems, 2008 Vol. 14 (2008), No. 3 (July), 409--439. (PDF file)


Maxwell strata in Euler's elastic problem, Journal of Dynamical and Control Systems, Vol. 14 (2008), No. 2 (April), 169--234. (PDF file)


Control Theory on Lie Groups, Journal Math. Sci., Vol. 156, No. 3, 2009, 381-439. (English, PDF file) (Russian, PDF file)


Optimality of Euler's elasticae, Doklady Mathematics, Vol. 76 (2007), No. 3, 817--819. (PDF file)


Controlability and symmetries of invariant systems on Lie groups and homogeneous spaces, in Russian, Fizmatlit Publishers, 2007 (242 pages). (PDF file)


Complete description of the Maxwell strata in the generalized Dido problem, Sbornik: Mathematics, 197 (2006), 6: 901--950. (PDF file)


The Maxwell set in the generalized Dido problem, Sbornik: Mathematics, 197 (2006), 4: 595--621. (PDF file)


Discrete symmetries in generalized Dido's problem, Sbornik: Mathematics, 197 (2006), 2: 235--257. (PDF file)


Geometric Control Theory (with A.A. Agrachev), in Russian, Fizmatlit Publishers, 2004. (PDF file)


Control Theory from the Geometric Viewpoint (with A.A. Agrachev), Preprint SISSA 77/2002/M, November 2002, SISSA, Trieste, Italy, published in Springer-Verlag, 2004. (PDF file)


Symmetries of Flat Rank Two Distributions and Sub-Riemannian Structures, Transactions of the American Mathematical Society, vol. 356 (2004), pp. 457-494. (PDF file)


Exponential mapping in the generalized Dido problem (in Russian), Matem. Sbornik, vol. 194 (2003), No. 9, pp. 63-90. (PDF file)


Geometric meaning of invariants in the generalized Dido problem (in Russian), with E. F. Sachkova, Proceedings of the University of Pereslavl, 2004. (ps file)


Optimal control problem for a nonlinear driftless 5-dimensional system with 2 inputs (with A. Agrachev), Proceedings of 5th IFAC Symposium NOLCOS 2001, St. Petersburg, July 2001. (ps file)


Classification of controllable systems on low-dimensional solvable Lie groups , Journal of Dynamical and Control Systems, 6 (2000), 2: 159--217. (ps file)


An Intrinsic Approach to the Control of Rolling Bodies (with A. Agrachev), Proceedings of the 38-th IEEE Conference on Decision and Control, Phoenix, Arizona, USA, December 7--10, 1999, vol.~1, 431--435 (ps file)


Controllability of Invariant Systems on Lie Groups and Homogeneous Spaces, Controllability of Invariant Systems on Lie Groups and Homogeneous Spaces, J. Math. Sci., v. 100, No. 4, 2000, 2355--2427. (ps file)


On Invariant Orthants of Bilinear Systems, Journal of Dynamical and Control Systems, 4 (1998), 1: 137--147. (ps file)


On Positive Orthant Controllability of Bilinear Systems in Small Codimensions, SIAM Journ. Control and Optimization, 35 (1997), 1: 29--35.


Controllability of Right-Invariant Systems on Solvable Lie Groups, Journal of Dynamical and Control Systems, 3 (1997), 4: 531--564. (ps file)


Controllability of Hypersurface and Solvable Invariant Systems, Journal of Dynamical and Control Systems, 2 (1996), 1: 55--67. (ps file)


Invariant Orthants of Bilinear Systems, Differentcialnije uravnenija, 31 (1995), 6: 1094--1095 (in Russian, translated into English in Differential equations)

Positive Orthant Controllability of Single-input Bilinear Systems, Mat. zametki, 85 (1995), 3: 419--424 (in Russian, translated into English in Mathematical Notes).


Positive Orthant Controllability of 2-dimensional and 3-dimensional Bilinear Systems, Differentcialnije Uravnenija, (1993), 2: 361--363 (in Russian, translated into English in Differential Equations).


Invariant Domains of 3-dimensional Bilinear Systems, Vestnik Moskovskogo Universiteta, Ser. Math. Mech., (1991), 4: 23--26 (in Russian, translated into English in Moscow University Mathematics Bulletin).


Controllability of 3-dimensional Bilinear Systems, Vestnik Moskovskogo Universiteta, Ser. Math. Mech., (1991), 3: 26--30 (in Russian, translated into English in Moscow University Mathematics Bulletin).


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sachkov@sys.botik.ru