Contrôlabilité des Systèmes non Linéaires

Abstract

Previous article Contrôlabilité des Systèmes non LinéairesClaude LobryClaude Lobryhttps://doi.org/10.1137/0308042PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Claude Chevalley, Theory of Lie Groups. I, Princeton Mathematical Series, vol. 8, Princeton University Press, Princeton, N. J., 1946ix+217 MR0015396 0063.00842 CrossrefGoogle Scholar[2] Wei-Liang Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Math. Ann., 117 (1939), 98–105 10.1007/BF01450011 MR0001880 0022.02304 CrossrefGoogle Scholar[3] A. F. Filippov, On certain questions in the theory of optimal control, J. SIAM Control Ser. A, 1 (1962), 76–84 10.1137/0301006 MR0149985 0139.05102 LinkGoogle Scholar[4] Hubert Halkin, A generalization of LaSalle's “bang-bang” principle, J. Soc. Indust. Appl. Math. Ser. A Control, 2 (1964), 199–202 MR0175691 0163.33003 LinkGoogle Scholar[5] Hubert Halkin, On a generalization of a theorem of Lyapunov, J. Math. Anal. Appl., 10 (1965), 325–329 10.1016/0022-247X(65)90127-7 MR0173959 0133.07801 CrossrefISIGoogle Scholar[6] Hubert Halkin, Mathematical foundations of system optimizationTopics in Optimization, Academic Press, New York, 1967, 197–262 MR0211784 CrossrefGoogle Scholar[7] Robert Hermann, On the accessibility problem in control theoryInternat. Sympos. Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, 325–332 MR0149402 0142.36102 CrossrefGoogle Scholar[8] Robert Hermann, The differential geometry of foliations. II, J. Math. Mech., 11 (1962), 303–315 MR0142131 0152.20502 ISIGoogle Scholar[9] Robert Hermann, Differential geometry and the calculus of variations, Mathematics in Science and Engineering, Vol. 49, Academic Press, New York, 1968x+440 MR0233313 0219.49023 Google Scholar[10] H. Hermes, Controllability and the singular problem, J. Soc. Indust. Appl. Math. Ser. A Control, 2 (1964), 241–260 MR0173572 0163.10803 LinkGoogle Scholar[11] G. W. Haynes and , H. Hermes, Nonlinear controllability via Lie theory, SIAM J. Control, 8 (1970), 450–460 10.1137/0308033 MR0277859 0229.93012 LinkISIGoogle Scholar[12] H. Hermes, Attainable sets and generalized geodesic spheres, J. Differential Equations, 3 (1967), 256–270 10.1016/0022-0396(67)90030-7 MR0207431 0155.42602 CrossrefISIGoogle Scholar[13] R. E. Kalman, , Y. C. Ho and , K. S. Narendra, Controllability of linear dynamical systems, Contributions to Differential Equations, 1 (1963), 189–213 MR0155070 0151.13303 Google Scholar[14] Jan Kučera, Solution in large of control problem $\dot x=(A(1-u)+Bu)x$, Czechoslovak Math. J., 16 (91) (1966), 600–623 MR0226102 0207.46902 ISIGoogle Scholar[15] Jan Kučera, Solution in large of control problem $\dot x=(Au+Bv)x$, Czechoslovak Math. J., 17 (92) (1967), 91–96 MR0226103 0189.15701 ISIGoogle Scholar[16] J. P. LaSalle, The time optimal control problemContributions to the theory of nonlinear oscillations, Vol. V, Princeton Univ. Press, Princeton, N.J., 1960, 1–24 MR0145169 0095.29503 Google Scholar[17] C. Lobry, Séminaire d'analyse numérique, Grenoble, 1968 Google Scholar[18] Yozô Matsushima, Groupes de Lie, Polycopié, Universite de Grenoble, Service de Mathematiques pures, 1966 Google Scholar[19] G. De Rham, Variétés différentiables, Hermann, Paris, 1960 0089.08105 Google Scholar[20] Pierre Samuel, Théorie algébrique des nombres, Hermann, Paris, 1967, 130– MR0215808 0146.06402 Google Scholar[21] Oscar Zariski and , Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960x+414 MR0120249 0121.27801 CrossrefGoogle Scholar[22] Jean Martinet, Masters Thesis, Sur les singularités des formes différentielles, Thése, Grenoble, 1969 Google Scholar[23] D. Luna, Stratifications, Séminaire, Grenoble, 1969 Google Scholar[24] Richard L. Bishop and , Richard J. Crittenden, Geometry of manifolds, Pure and Applied Mathematics, Vol. XV, Academic Press, New York, 1964ix+273 MR0169148 0132.16003 Google Scholar Previous article FiguresRelatedReferencesCited ByDetails A Sufficient Condition for Small-Time Local ControllabilitySIAM Journal on Control and Optimization, Vol. 48, No. 4 | 8 July 2009AbstractPDF (337 KB)Dubins' Problem on Surfaces II: Nonpositive CurvatureSIAM Journal on Control and Optimization, Vol. 45, No. 2 | 26 July 2006AbstractPDF (279 KB)Controllability of Poisson SystemsSIAM Journal on Control and Optimization, Vol. 43, No. 3 | 26 July 2006AbstractPDF (213 KB)On the Global Controllability of Nonlinear Systems: Fountains, Recurrence, and Applications to Hamiltonian SystemsSIAM Journal on Control and Optimization, Vol. 41, No. 5 | 26 July 2006AbstractPDF (251 KB)A Characterization of the Lie Algebra Rank Condition by Transverse Periodic FunctionsSIAM Journal on Control and Optimization, Vol. 40, No. 4 | 26 July 2006AbstractPDF (243 KB)Design of Homogeneous Time-Varying Stabilizing Control Laws for Driftless Control