References
Ph. Adda, “Contrôllabilité des systèmes bilinéaires generaux et homogenes dans ℝ2,” Lect. Notes Contr. Inf. Sci., 111, 205–214 (1988).
Ph. Adda and G. Sallet, “Determination algorothmique de la contrôllabilité pour des families finies de champs de vecteurs lineaires sur ℝ2\{0}, R.A.I.R.O. APII, 24, 377–390 (1990).
A. A. Agrachev, “Local controllability and semigroups of diffeomorphisms,” Acta Appl. Math., 32, 1–57 (1993).
A. A. Agrachev, S. V. Vakhrameev, and R. V. Gamkrelidze, “Differential-geometric and group-theoretic methods in optimal control theory,” in: Progress in Science and Technology, Series on Problems in Geometry [in Russian], Vol. 14, All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1983), pp. 3–56.
H. Albuquerque and F. Silva Leite, “On the generators of semisimple Lie algebras,” Linear Algebra Appl., 119, 51–56 (1989).
Yu. N. Andreev, “Differential-geometric methods in control theory,” Automat. Telemekh., No. 10, 5–46 (1982).
R. El Assoudi, “Accessibilité par des champs de vecteurs invariants à droite sur un groupe de Lie,” Thèse de doctorat de l’Université Joseph Fourier, Grenoble (1991).
R. El Assoudi and J. P. Gauthier, “Controllability of right-invariant systems on real simple Lie groups of type F 4, G 2, C n, and B n” Math. Control Signals Systems, 1, 293–301 (1988).
R. El Assoudi and J. P. Gauthier, “Controllability of right-invariant systems on semi-simple Lie groups,” in: New Trends in Nonlinear Control Theory, Springer-Verlag 122 (1989), pp. 54–64.
R. El Assoudi, J. P. Gauthier, and I. Kupka, “On subsemigroups of semisimple Lie groups,” Ann. Inst. Henri Poincaré, 13, No. 1, 117–133 (1996).
L. Auslander, L. Green, and F. Hahn, “Flows on homogeneous spaces,” Ann. Math. Studies, No. 53, Princeton Univ. Press, Princeton, New Jersey (1963).
V. Ayala Bravo, “Controllability of nilpotent systems,” in: Geometry in Nonlinear Control and Differential Inclusions, Banach Center Publications, Warszawa, 32 (1995), pp. 35–46.
V. Ayala Bravo and L. Vergara, “Co-adjoint representation and controllability,” Proyecciones, 11, 37–48 (1992).
V. Ayala Bravo and I. Jiron, “Observabilidad del producto directo de sistemas bilineales,” Revista Cubo, 9, 35–46 (1993).
V. Ayala Bravo and J. Tirao, “Controllability of linear vector fields on Lie groups,” Int. Centre Theor. Physics, Preprint IC/95/310, Trieste, Italy (1994).
V. Ayala Bravo and A. Hacibekiroglu, “Observability of linear systems on Lie groups,” Int. Centre Theor. Physics, Preprint IC/95/2, Trieste, Italy (1995).
V. Ayala Bravo, O. Rojo, and R. Soto, “Observability of the direct product of bilinear systems on Lie groups,” Comput. Math. Appl., 36, No. 3, 107–112 (1998).
J. Basto Gonçalves, “Sufficient conditions for local controllability with unbounded controls,” SIAM J. Control Optim., 16, 1371–1378 (1987).
J. Basto Gonçalves, “Controllability in codimension one,” J. Diff. Equat., 68, 1–9 (1987).
J. Basto Gonçalves, “Local controllability in 3-manifolds,” Syst. Contr. Lett., 14, 45–49 (1990).
J. Basto Gonçalves, “Local controllability of scalar input systems on 3-manifolds,” Syst. Contr. Lett., 16, 349–355 (1991).
A. Bacciotti, “On the positive orthant controllability of two-dimensional bilinear systems,” Syst. Contr. Lett., 3, 53–55 (1983).
A. Bacciotti and G. Stefani, “On the relationship between global and local controllability,” Math. Syst. Theory, 16, 79–91 (1983).
R. M. Bianchini and G. Stefani, “Sufficient conditions of local controllability,” in: Proc. 25th IEEE Conf. Decis. Control, Athens (1986).
B. Bonnard, “Contrôllabilité des systèmes bilinéaires,” Math. Syst. Theory, 15, 79–92 (1981).
B. Bonnard, “Contrôllabilité des systèmes bilinéaires,” in: Qutils Modeles Math. Autom. Anal. Syst. Trait Signal., Vol. 1, Paris (1981), pp. 229–243.
B. Bonnard, “Controllabilité de systèmes mecaniques sur les groupes de Lie,” SIAM J. Control Optim., 22, 711–722 (1984).
B. Bonnard, V. Jurdjevic, I. Kupka, and G. Sallet, “Transitivity of families of invariant vector fields on the semidirect products of Lie groups,” Trans. Amer. Math. Soc., 271, No. 2, 525–535 (1982).
W. Boothby, “A transitivity problem from control theory,” J. Diff. Equat., 17, 296–307 (1975).
W. M. Boothby, “Some comments on positive orthant controllability of bilinear systems,” SIAM J. Control Optim., 20, 634–644 (1982).
W. Boothby and E. N. Wilson, “Determination of the transitivity of bilinear systems,” SIAM J. Control, 17, 212–221 (1979).
A. Borel, “Some remarks about transformation groups transitive on spheres and tori,” Bull. Amer. Math. Soc., 55, 580–586 (1949).
A. Borel, “Le plan projectif des octaves et les sphères comme espaces homogènes,” C. R. Acad. Sci. Paris, 230, 1378–1380 (1950).
N. Bourbaki, Éléments de Mathématique, Groupes et Algèbres de Lie, Chapitre 2: Algèbres de Lie, Hermann, Paris (1960).
N. Bourbaki, Éléments de Mathématique, Groupes et Algèbres de Lie, Chapitre 2: Algèbres de Lie Libres. Chapitre 3: Groupes de Lie, Hermann, Paris (1972).
R. W. Brockett, “System theory on group manifolds and coset spaces,” SIAM J. Control, 10, 265–284 (1972).
R. W. Brockett, “Lie algebras and Lie groups in control theory,” in: Geometric Methods in System Theory, D. Q. Mayne and R. W. Brockett, eds., Proceedings of the NATO Advanced study institute held at London, August 27–September 7, 1983, Dordrecht-Boston, D. Reidel Publishing Company (1973), pp. 43–82.
R. W. Brockett, “On the reachable set for bilinear systems,” Lect. Notes Econ. Math. Syst., 111, 54–63 (1975).
C. Bruni, G. Di Pillo, and G. Koch, “Bilinear systems: an appealing class of ‘nearly linear’ systems in theory and applications,” IEEE Trans. Autom. Control, 19, 334–348 (1974).
J. L. Casti, “Recent developments and future perspectives in nonlinear system theory,” SIAM Review, 24, No. 2, 301–331 (1982).
D. Cheng, W. P. Dayawansa, and C. F. Martin, “Observability of systems on Lie groups and coset spaces,” SIAM J. Control Optim., 28, 570–581 (1990).
I. Chong and J. D. Lawson, “Problems on semigroup and control,” Semigroup Forum, 41, 245–252 (1990).
P. Crouch and F. Silva Leite, “On the uniform finite generation of SO(n; ℝ),” Syst. Contr. Letters, 2, 341–347 (1983).
P. Crouch and C. I. Byrnes, “Symmetries and local controllability,” in: Algebraic and Geometric Methods in Nonlinear Control Theory, M. Fliess and M. Hazewinkel, eds., Reidel Publishing Company, Holland (1986).
D. Elliott and T. Tarn, “Controllability and observability for bilinear systems,” in: SIAM National Meeting, Seattle, Washington (1971).
M. J. Enos, “Controllability of a system of two symmetric rigid bodies in three space,” SIAM J. Control Optim., 32, 1170–1185 (1994).
J. P. Gauthier, Structures des Systemes Nonlineares, GNRS, Paris (1984).
J. P. Gauthier and G. Bornard, “Contrôlabilité des systèmes bilinèaires,” SIAM J. Control Optim., 20, No. 3, 377–384 (1982).
J. P. Gauthier, I. Kupka and G. Sallet, “Controllability of right invariant systems on real simple Lie groups,” Syst. Contr. Lett., 5, 187–190 (1984).
R. Hermann, “On the accessibility problem in control theory,” in: International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York (1963), pp. 325–332.
H. Hermes, “On local and global controllability,” SIAM J. Control, 12, 252–261 (1974).
H. Hermes, “Controlled stability,” Ann. Mat. Pura Appl., CXIV, 103–119 (1977).
H. Hermes, “On local controllability,” SIAM J. Control Optim., 20, 211–220 (1982).
H. Hermes and M. Kawski, “Local controllability of a single-input, affine system,” in: Proc. 7th Int. Conf. Nonlinear Analysis, Dallas (1986).
J. Hilgert, “Maximal semigroups and controllability in products of Lie groups,” Arch. Math., 49, 189–195 (1987).
J. Hilgert, “Controllability on real reductive Lie groups,” Math Z., 209, 463–466 (1992).
J. Hilgert, K. H. Hofmann and J. D. Lawson, “Controllability of systems on a nilpotent Lie group,” Beiträge Algebra Geometrie, 20, 185–190 (1985).
J. Hilgert, K. H. Hofmann and J. D. Lawson, Lie Groups, Convex Cones, and Semigroups, Oxford University Press (1989).
J. Hilgert and K. H. Neeb, “Lie semigroups and their applications,” Lect. Notes Math., 1552 (1993).
M. W. Hirsch, “Convergence in neural nets,” in: Proc. Int. Conf. Neural Networks, Vol. II (1987), pp. 115–125.
R. M. Hirschorn, “Invertibility of control systems on Lie groups,” SIAM J. Contr. Optim., 15, 1034–1049 (1977).
K. H. Hofmann, “Lie algebras with subalgebras of codimension one,” Ill. J. Math., 9, 636–643 (1965).
K. H. Hofmann, “Hyperplane subalgebras of real Lie algebras,” Geom. Dedic., 36, 207–224 (1990).
K. H. Hofmann, “Compact elements in solvable real Lie algebras,” Seminar Sophus Lie (Lie theory), 2, 41–55 (1992).
K. H. Hofmann, “Memo to Yurii Sachkov on Hyperplane Subalgebras of Lie Algebras,” E-mail message, March (1996).
K. H. Hofmann and J. D. Lawson, “Foundations of Lie semigroups,” Lect. Notes Math., 998, 128–201 (1983).
K. R. Hunt, “Controllability of nonlinear hypersurface systems,” in: C. I. Byrnes and C. F. Martin, eds., Algebraic and Geometric Methods in Linear Systems Theory, AMS, Providence, Rhode Island (1980).
K. R. Hunt, “n-Dimensional controllability with (n−1) controls,” IEEE Trans. Autom. Control, 27, 113–117 (1982).
N. Imbert, M. Clique, and A.-J. Fossard, “Un critère de gouvernabilite des systèmes bilinéaires,” R.A.I.R.O., 3, 55–64 (1975).
A. Isidori, Nonlinear Control Systems. An Introduction, Springer, Berlin (1989).
N. Jacobson, Lie Algebras, Interscience Publishers, New York-London (1962).
I. Joo, N. M. Tuan, “On controllability of some bilinear systems,” C. R. Acad. Sci., Ser. I, 315, 1393–1398 (1992).
A. Joseph, “The minimal orbit in a simple Lie algebra and its associated maximal ideal,” Ann. Sci. l'École Norm. Sup., 9, No. 1, 1–29 (1976).
V. Jurdjevic, On the reachability properties of curves in ℝn with prescribed curvatures, University of Bordeaux Publ. 1, No. 8009 (1980).
V. Jurdjevic, “Optimal control problems on Lie groups,” in: Analysis of Controlled Dynamical Systems, Proc. Confer., Lyon, France, July 1990, B. Bonnard, B. Bride, J. P. Gauthier, and I. Kupka, eds., pp. 274–284.
V. Jurdjevic, “The geometry of the plate-ball problem,” Arch. Rat. Mech. Anal., 124, 305–328 (1993).
V. Jurdjevic, “Optimal control problems on Lie groups: Crossroads between geometry and mechanics,” in: Geometry of Feedback and Optimal Control, B. Jukubczyk and W. Respondek, eds., Marcel Dekker, New York (1993).
V. Jurdjevic, “Non-Euclidean elastica,” Amer. J. Math., 117, 93–124 (1995).
V. Jurdjevic, Geometric Control Theory, Cambridge University Press (1997).
V. Jurdjevic and I. Kupka, “Control systems subordinated to a group action: Accessibility,” J. Differ. Equat., 39, 186–211 (1981).
V. Jurdjevic and I. Kupka, “Control systems on semi-simple Lie groups and their homogeneous spaces,” Ann. Inst. Fourier, Grenoble, 31, No. 4, 151–179 (1981).
V. Jurdjevic and G. Sallet, “Controllability properties of affine systems,” SIAM J. Control, 22, 501–508 (1984).
V. Jurdjevic and H. Sussmann, “Control systems on Lie groups,” J. Diff. Equat., 12, 313–329 (1972).
M. Kawski, Nilpotent Lie Algebras of Vector Fields and Local Controllability of Nonlinear Systems, Ph.D. Dissertation, Univ. of Colorado, Boulder (1986).
D. E. Koditschek and K. S. Narendra, “The controllability of planar bilinear systems,” IEEE Trans. Autom. Control. 30, 87–89 (1985).
A. Krener, “A generalization of Chow’s theorem and the Bang-Bang theorem to non-linear control problems,” SIAM J. Control, 12, 43–51 (1974).
P. S. Krishnaprasad and D. P. Tsakiris, “G-suakes: Nonholonomic kinematic chains on Lie groups,” Proc. 33rd IEEE Conf. Decis. Control, Lake Buena Vista, FL (1994), pp. 2955–2960.
P. S. Krishnaprasad and D. P. Tsakiris, “Oscillations, SE(2)-snakes and motion control,” Proc. 34th IEEE Conf. Decis. and Control, New Orleans, Louisiana (1995).
J. Kučera, “Solution in the large of the control system ẋ=(Au+Bu)x,” Czech. Math. J., 16, 600–623 (1966).
J. Kučera, “Solution in the large of the control system ẋ=(Au+Bu)x,” Czech. Math. J., 17, 91–96 (1967).
J. Kučera, “On the accessibility of bilinear systems,” Czech. Math. J., 20, 160–168 (1970).
I. Kupka, “Applications of semigroups to geometric control theory,” in: The Analytical and Topological Theory of Semigroups—Trends and Developments, K. H. Hofmann, J. D. Lawson, and J. S. Pym, eds., de Gruyter Expositions in Mathematics, 1 (1990), pp. 337–345.
M. Kuranishi, “On everywhere dense imbedding of free groups in Lie groups,” Nagoya Math. J., 2 63–71 (1951).
J. D. Lawson, “Maximal subsemigroups of Lie groups that are total,” Proc. Edinburgh Math. Soc., 30, 479–501 (1985).
N. Levitt and H. J. Sussmann, “On controllability by means of two vector fields,” SIAM J. Control, 13, 1271–1281 (1975).
N. L. Lepe, “Geometric method of investigation of controllability of two-dimensional bilinear systems,” Avtomat. Telemekh., No. 11, 19–25 (1984).
C. Lobry, “Contrôllabilité des systèmes non linéaires,” SIAM J. Control, 8, 573–605 (1970).
C. Lobry, “Controllability of non linear systems on compact manifolds,” SIAM J. Control, 12, 1–4 (1974).
C. Lobry, “Critères de gouvernabilite des asservissements non linéaires,” R.A.I.R.O., 10, 41–54 (1976).
L. Markus, “Controllability of multi-trajectories on Lie groups,” Lect. Notes Math., 898, 250–256 (1981).
D. Mittenhuber, “Kontrolltheorie auf Lie-Gruppen,” Seminar Sophus Lie, 1, 185–191 (1991).
D. Mittenhuber, “Semigroups in the simply connected covering of SL(2)”, Semigroup Forum, 46, 379–387 (1993).
D. Mittenhuber, “Control theory on Lie groups, Lie semigroups and the globality of Lie wedges,” Ph.D. Dissertation, TH Darmstadt (1994).
F. Monroy-Pérez, “Non-Euclidean Dubins' problem,” J. Dyn. Cont. Syst., 4, 249–272 (1998).
D. Montgomery and H. Samelson, “Transformation groups of spheres,” Ann. Math., 44, 454–470 (1943).
N. E. Leonard, “Averaging and motion control of systems on Lie groups,” Ph.D. dissertation, Univ. Maryland, College Park, MD (1994).
N. E. Leonard and P. S. Krishnaprasad, “Control of switched electrical networks using averaging on Lie groups,” Proc. 33rd IEEE Conf. Decis. Control, Lake Buena Vista, FL (1994), pp. 1919–1924.
N. E. Leonard and P. S. Krishnaprasad, “Motion control of drift-free, left-invariant systems on Lie groups,” IEEE Trans. Autom. Control, 40, 1539–1554 (1995).
M. Lovric, “Left-invariant control systems on Lie groups,” Preprint F193-CT03, January 1993, The Fields Institute for Research in Mathematical Sciences, Canada.
K.-H. Neeb, “Semigroups in the universal covering of SL(2),” Semigroup Forum, 40, 33–43 (1990).
U. Piechottka, “Comments on ‘The controllability of planar bilinear systems,” IEEE Trans. Autom. Control, 35, 767–768 (1990).
U. Piechottka and P. M. Frank, “Controllability of bilinear systems: A survey and some new results,” in: Nonlinear Control Systems Design, A Isidori, ed., Pergamon Press (1990), pp. 12–28.
R. E. Rink and R. R. Möhler, “Completely controllable bilinear systems,” SIAM, J. Control, 6, 477–486 (1986).
Yu. L. Sachkov, “Controllability of three-dimensional bilinear systems,” Vestn. MGU, Mat., Mekh., No. 4, 26–30 (1991).
Yu. L. Sachkov, “Invariant domains of three-dimensional bilinear systems,” Vestn. MGU, Mat., Mekh., No. 2, 361–363 (1993).
Yu. L. Sachkov, “Positive orthant controllability of 2-dimensional and 3-dimensional bilinear systems,” Diff. Uravn., No. 2, 361–363 (1993).
Y. L. Sachkov, “Positive orthant controllability of single-input bilinear systems,” Mat. Zametki, 85, 419–424 (1995).
Yu. L. Sachkov, “Controllability of hypersurface and solvable invariant systems,” J. Dyn. Control Syst., 2, No. 1, 55–67 (1996).
Yu. L. Sachkov, “On positive orthant controllability of bilinear systems in small codimensions,” SIAM J. Control Opt., 35, 29–35 (1997).
Yu. L. Sachkov, “Controllability of right-invariant systems on solvable Lie groups,” J. Dyn. Control Syst., 3, No. 4, 531–564 (1997).
Yu. L. Sachkov, “On invariant orthants of bilinear systems,” J. Dyn. Control Syst., 4, No. 1, 137–147 (1998).
Yu. L. Sachkov, “Survey on controllability of invariant systems on solvable Lie Groups,” in: Proc. AMS Summer Research Institute on Differential Geometry and Control, Boulder, Colorado, July 1997, to appear.
Yu. L. Sachkov, “Classification of controllability in small-dimensional solvable Lie algebras” (in preparation).
G. Sallet, “Une condition suffisante de complète contrôlabilité dans le groupe des déplacements de ℝn” C. R. Acad. Sc. Paris, Série A, 282, 41–44 (1976).
G. Sallet, “Complete controllabilite sur les groupes lineaires,” in: Qutils Modeles Math. Autom. Anal. Syst. Trait Signal, Vol. 1, Paris (1981), pp. 215–227.
G. Sallet, “Extension techniques,” in: Systems and Control Encyclopedia II (1987), pp. 1581–1583.
G. Sallet, “Lie groups: Controllability,” in: Systems and Control Encyclopedia (1987), pp. 2756–2759.
H. Samelson, “Topology of Lie groups,” Bull. Amer. Math. Soc., 58, 2–37 (1952).
L. A. B. San Martin, “Invariant control sets on flag manifolds,” Math. Control Signals Systems, 6, 41–61 (1993).
L. A. B. San Martin and P. A. Tonelli, “Semigroup actions on homogeneous spaces,” Semigroup Forum, 14, 1–30 (1994).
A. Sarti, G. Walsh, and S. Sastry, “Steering left-invariant control systems on matrix Lie groups,” in: Proc. 32nd IEEE Conf. Decis. Control, San Antonio, Texas (1993), pp. 3117–3121.
F. Silva Leite, “Uniform controllable sets of left-invariant vector fields on compact Lie groups,” Syst. Contr. Lett., 6, 329–335 (1986).
F. Silva Leite, “Uniform controllable sets of left-invariant vector fields on noncompact Lie groups,” Syst. Contr. Lett., 7, 213–216 (1986).
F. Silva Leite, “Pairs of generators for compact real forms of the classical Lie algebras,” Linear Algebra Appl., 121, 123–133 (1989).
F. Silva Leite, “Bounds on the order of generation of SO(n;ℝ) by one-parameter subgroups,” Rocky Mount. J. Math., 21, 879–911 (1991).
F. Silva Leite and P. Crouch, “Controllability on classical Lie groups,” Math. Control Signals Systems, 1, 31–42 (1988).
G. Stefani, “On the local controllability of a scalar-input system,” in: Theory and Applications of Nonlinear Control Systems, C. I. Byrnes and A. Lindquist, eds., Elsevier (1986).
H. J. Sussmann, “The ‘Bang-Bang’ problem for certain control systems on GL(n;ℝ),” SIAM J. Control, 10, 470–476 (1972).
H. J. Sussmann and V. Jurdjevic, “Controllability of non-linear systems,” J. Diff. Equat., 12, 95–116 (1972).
H. J. Sussmann, “Orbits of families of vector fields and integrability of distributions,” Trans. Amer. Math. Soc., 180, 171–188 (1973).
H. J. Sussmann, “Lie brackets, real analyticity and geometric control,” in: Differential Geometric Control Theory, R. W. Brockett, R. S. Millmann, and H. J. Sussmann, eds., Birkhäuser, Boston-Basel-Stuttgart (1983), pp. 1–116.
H. J. Sussmann, “A general theorem on local controllability,” SIAM J. Control Optim., 25, 158–194 (1987).
A. I. Tretyak, “Sufficient conditions for local controllability and high-order necessary conditions for optimality. A differential-geometric approach,” in: Progress in Science and Technology, Series on Mathematics and Its Applications. Thematical Surveys, Vol. 24, Dynamical Systems-4 [in Russian], All-Russian Institute for Scientific and Technical Information (VINITI), Ross. Akad. Nauk (1996).
S. A. Vakhrameev, “Geometrical and topological methods in optimal control theory,” J. Math. Sci., 76, No. 5, 2555–2719 (1995).
S. A. Vakhrameev and A. V. Sarychev, “Geometrical control theory,” in: Progress in Science and Technology, series on Algebra, Topology, and Geometry. Thematical Surveys, Vol. 23 [in Russian], All-Russian Institute for Scientific and Technical Information (VINITI), Ross. Akad. Nauk (1985), pp. 197–280.
V. S. Varadarjan, Lie Groups, Lie Algebras, and Their Representations, Springer-Verlag, New York-Berlin-Heidelberg-Tokyo (1984).
E. B. Vinberg and A. L. Onishchik, Seminar on Lie Groups and Algebraic Groups [in Russian], Moscow (1988).
E. B. Vinberg, V. V. Gorbatcevich, and A. L. Onishchik, “Construction of Lie groups and Lie algebras,” in: Progress in Science and Technology, Series on Complementary Problems in Mathematics, Basic Directions, Vol. 41, All-Russian Institute for Scientific and Technical Information (VINITI), Ross. Akad. Nauk (1989).
G. Walsh, R. Montgomery, and S. Sastry, “Optimal path planning on matrix Lie groups”, Proc. 33rd IEEE Conf. Decis. and Control, Lake Buena Vista, FL (1994), pp. 1312–1318.
G.N. Yakovenko, “Optimal control synthesis on a third-order Lie group”, Kybern. Vychisl. Tekh. (Kiev), 51, 17–22 (1981).
G.N. Yakovenko, “Control on Lie groups: First integrals, singular controls”, Kybern. Vychisl. Tekh. (Kiev), 62, 10–20 (1984).
V.A. Yatcenko, “Euler equation on Lie groups and optimal control of bilinear systems”, Kybern. Vychisl. Tekh. (Kiev), 58, 78–80 (1983).
M.I. Zelikin, “Optimal trajectories synthesis on representation spaces of Lie groups”, Mat. Sb., 132, 541–555 (1987).
M.I. Zelikin, “Group symmetry in degenerate extremal problems”, Usp. Mat. Nauk, 43, No. 2, 139–140 (1988).
M.I. Zelikin, “Optimal control of a rigid body rotation”, Dokl. Ross. Akad. Nauk, 346, 334–336 (1996).
M.I. Zelikin, “Totally extremal manifolds for optimal control problems”, in: Semigroups in Algebra, Geometry and Analysis, Hofmann, Lawson, and Vinberg, eds., Walter de Gruyter & Co., Berlin-New York (1995), pp. 339–354.
Additional information
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya, Tematicheskie Obzory. Vol. 59, Dinamicheskie Sistemy-8, 1998.
Rights and permissions
About this article
Cite this article
Sachkov, Y.L. Controllability of invariant systems on lie groups and homogeneous spaces. J Math Sci 100, 2355–2427 (2000). https://doi.org/10.1007/s10958-000-0002-8
Issue Date:
DOI: https://doi.org/10.1007/s10958-000-0002-8