Controllability of invariant systems on lie groups and homogeneous spaces

[1]  Velimir Jurdjevic The geometry of the plate-ball problem , 1993 .

[2]  F. Monroy-Pérez,et al.  Non-Euclidean Dubins' Problem , 1998 .

[3]  V. Jurdjevic NON-EUCLIDEAN ELASTICA , 1995 .

[4]  H. Samelson,et al.  Topology of Lie groups , 1952 .

[5]  Bernard Bonnard,et al.  Transitivity of families of invariant vector fields on the semidirect products of Lie groups , 1982 .

[6]  H. Sussmann,et al.  Control systems on Lie groups , 1972 .

[7]  J. Hilgert,et al.  Lie semigroups and their applications , 1993 .

[8]  On the uniform finite generation of SO(n, R) , 1983 .

[9]  M. Hirsch CONVERGENCE IN NEURAL NETS. , 1987 .

[10]  C. Lobry Controllability of Nonlinear Systems on Compact Manifolds , 1974 .

[11]  William M. Boothby Some Comments on Positive Orthant Controllability of Bilinear Systems , 1982 .

[12]  H. Hermes On Local and Global Controllability , 1974 .

[13]  R. El Assoudi,et al.  Controllability of right invariant systems on real simple Lie groups of typeF4,G2,Cn, andBn* , 1988, Math. Control. Signals Syst..

[14]  MAXIMAL SUBSEMIGROUPS OF LIE GROUPS THAT ARE TOTAL , 1987 .

[15]  C. Bruni,et al.  Bilinear systems: An appealing class of "nearly linear" systems in theory and applications , 1974 .

[16]  I. Chon,et al.  Problems on semigroups and control , 1990 .

[17]  P. Krishnaprasad,et al.  G-snakes: nonholonomic kinematic chains on Lie groups , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[18]  V. Varadarajan Lie groups, Lie algebras, and their representations , 1974 .

[19]  A. Krener A Generalization of Chow’s Theorem and the Bang-Bang Theorem to Nonlinear Control Problems , 1974 .

[20]  Andrei A. Agrachev,et al.  Local controllability and semigroups of diffeomorphisms , 1993 .

[21]  Roger W. Brockett,et al.  On the Reachable Set for Bilinear Systems , 1975 .

[22]  On accessibility of bilinear systems , 1970 .

[23]  S. Sastry,et al.  Steering left-invariant control systems on matrix Lie groups , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[24]  J. Hilgert Maximal semigroups and controllability in products of Lie groups , 1987 .

[25]  R. Bianchini,et al.  Sufficient conditions of local controllability , 1986, 1986 25th IEEE Conference on Decision and Control.

[26]  Bernard Bonnard Controlabilite de Systemes Mecaniques Sur Les Groupes de Lie , 1984 .

[27]  Uniform controllable sets of left-invariant vector fields on noncompact lie groups , 1986 .

[28]  A. Joseph,et al.  The minimal orbit in a simple Lie algebra and its associated maximal ideal , 1976 .

[29]  Pedro A. Tonelli,et al.  Semigroup actions on homogeneous spaces , 1995 .

[30]  V. Jurdjevic,et al.  Control systems subordinated to a group action: Accessibility , 1981 .

[31]  Semigroups in the simply connected covering of SL(2) , 1993 .

[32]  H. Sussmann,et al.  Controllability of nonlinear systems , 1972 .

[33]  Luiz A. B. San Martin,et al.  Invariant control sets on flag manifolds , 1993, Math. Control. Signals Syst..

[34]  Naomi Ehrich Leonard,et al.  Control of switched electrical networks using averaging on Lie groups , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[35]  L. Markus,et al.  Controllability of multi-trajectories on Lie groups , 1981 .

[36]  Naomi Ehrich Leonard Averaging and Motion Control of Systems on Lie Groups , 1994 .

[37]  S. A. Vakhrameev Geometrical and topological methods in optimal control theory , 1995 .

[38]  Daizhan Cheng,et al.  Observability of systems on lie groups and coset spaces , 1990 .

[39]  J. Gauthier,et al.  On subsemigroups of semisimple Lie groups , 1996 .

[40]  S. Moran,et al.  N. Bourbaki, Éléments de Mathématique XXVI. Groupes et Algèbres de Lie: Chapitre 1. Algèbres de Lie (Hermann et cie), 148 pp., 21 NF. , 1962, Proceedings of the Edinburgh Mathematical Society.

[41]  Local controllability in 3-manifolds , 1990 .

[42]  H. Sussmann,et al.  On Controllability by Means of Two Vector Fields , 1975 .

[43]  Peter E. Crouch,et al.  Symmetries and Local Controllability , 1986 .

[44]  Y. Sachkov Controllability of Invariant Systems on Solvable Lie Groups , 1996 .

[45]  F. Leite Pairs of generators for compact real forms of the classical Lie algebras , 1989 .

[46]  R. Hermann On the Accessibility Problem in Control Theory , 1963 .

[47]  John L. Casti,et al.  Recent Developments and Future Perspectives in Nonlinear System Theory , 1982 .

[48]  A. Borel Some remarks about Lie groups transitive on spheres and tori , 1949 .

[49]  D. Montgomery,et al.  Transformation Groups of Spheres , 1943 .

[50]  O. Rojo,et al.  Observability of the direct product of bilinear control systems on lie groups , 1998 .

[51]  Louis R. Hunt,et al.  n -Dimensional controllability with (n-1) controls , 1982 .

[52]  Velimir Jurdjevic,et al.  Optimal Control Problems on Lie groups , 1991 .

[53]  Louis Auslander,et al.  Flows on Homogeneous Spaces , 1963 .

[54]  R. R. Mohler,et al.  Completely Controllable Bilinear Systems , 1968 .

[55]  William M. Boothby,et al.  Determination of the Transitivity of Bilinear Systems , 1979 .

[56]  Controllability in codimension one , 1987 .

[57]  Yuri L. Sachkov On Positive Orthant Controllability of Bilinear Systems in Small Codimensions , 1997 .

[58]  A. I. Tretiyak Sufficient conditions for local controllability and high-order necessary conditions for optimality. A differential-geometric approach , 1997 .

[59]  R. Brockett System Theory on Group Manifolds and Coset Spaces , 1972 .

[60]  J.Basto Gonçalves Local controllability of scalar input systems on 3-manifolds , 1991 .

[61]  F. S. Leite Bounds on the Order of Generation of ${\bf SO(n,\R)}$ by One-Parameter Subgroups , 1991 .

[62]  Velimir Jurdjevic,et al.  Control systems on semi-simple Lie groups and their homogeneous spaces , 1981 .

[63]  H. Sussmann A general theorem on local controllability , 1987 .

[64]  A. Isidori Nonlinear Control Systems , 1985 .

[65]  Y. Sachkov On Invariant Orthants of Bilinear Systems , 1998 .

[66]  Hyperplane subalgebras of real Lie algebras , 1990 .

[67]  Andrea Bacciotti On the positive orthant controllability of two-dimensional bilinear systems , 1983 .

[68]  H. Sussmann The “Bang-Bang” Problem for Certain Control Systems in $GL(n,R)$ , 1972 .

[69]  D. Elliott,et al.  Controllability and Observability for Bilinear Systems , 1971 .

[70]  Y. Sachkov Controllability of Right-Invariant Systems on Solvable Lie Groups , 1997 .

[71]  A. Isidori Nonlinear Control Systems: An Introduction , 1986 .

[72]  C. Lobry Contr^olabilite des systemes non lineaires , 1970 .

[73]  V. Jurdjevic Geometric control theory , 1996 .

[74]  Jan Kucera,et al.  Title: Solution in large of control problem $\dot x=(A(1-u)+Bu)x$ , 1966 .

[75]  Velimir Jurdjevic,et al.  Controllability properties of affine systems , 1984, The 23rd IEEE Conference on Decision and Control.

[76]  S. Sastry,et al.  Optimal path planning on matrix Lie groups , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[77]  R. M. Hirschorn Invertibility of Control Systems on Lie Groups , 1977 .

[78]  K. Hofmann,et al.  Foundations of lie semigroups , 1983 .

[79]  Daniel E. Koditschek,et al.  The controllability of planar bilinear systems , 1985, IEEE Transactions on Automatic Control.

[80]  J. Hilgert,et al.  Lie groups, convex cones, and semigroups , 1989 .

[81]  H. Sussmann Orbits of families of vector fields and integrability of distributions , 1973 .

[82]  J. Hilgert Controllability on real reductive Lie groups , 1992 .

[83]  J. Gauthier,et al.  Contrôlabilité des Systèmes Bilinéaires , 1982 .

[84]  P. Frank,et al.  CONTROLLABILITY OF BILINEAR SYSTEMS—A SURVEY AND SOME NEW RESULTS , 1989 .

[85]  Semigroups in the universal covering group of SL(2) , 1991 .

[86]  Naomi Ehrich Leonard,et al.  Motion control of drift-free, left-invariant systems on Lie groups , 1995, IEEE Trans. Autom. Control..

[87]  Classification of Controllable Systems on Low-Dimensional Solvable Lie Groups , 2000 .

[88]  William M. Boothby,et al.  A transitivity problem from control theory , 1975 .

[89]  D. E. Koditschek,et al.  Comments, with reply, on "The controllability of planar bilinear systems" by D.E. Koditschek and K.S. Narendra , 1990 .

[90]  Dimitris P. Tsakiris,et al.  Oscillations, SE(2)-snakes and motion control , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[91]  F. Silva,et al.  Controllability on classical Lie groups , 1988, Math. Control. Signals Syst..

[92]  V. Bravo Controllability of nilpotent systems , 1995 .

[93]  R. Brockett Lie Algebras and Lie Groups in Control Theory , 1973 .

[94]  Masatake Kuranishi,et al.  On Everywhere Dense Imbedding of Free Groups in Lie Groups , 1951, Nagoya Mathematical Journal.

[95]  J. Gauthier,et al.  Controllability of right invariant systems on real simple Lie groups , 1984 .

[96]  Henry Hermes On Local Controllability , 1982 .

[97]  Y. Sachkov Controllability of hypersurface and solvable invariant systems , 1996 .