Nonlinear Controllability via Lie Theory

Abstract

Previous article Next article Nonlinear Controllability via Lie TheoryG. W. Haynes and H. HermesG. W. Haynes and H. Hermeshttps://doi.org/10.1137/0308033PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] 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[2] 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[3] Robert Hermann, The differential geometry of foliations. II, J. Math. Mech., 11 (1962), 303–315 MR0142131 0152.20502 ISIGoogle Scholar[4] Robert Hermann, Some differential-geometric aspects of the Lagrange variational problem, Illinois J. Math., 6 (1962), 634–673 MR0145457 0196.54301 CrossrefGoogle Scholar[5] 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[6] 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 Next article FiguresRelatedReferencesCited ByDetails Controllability of Poisson SystemsSIAM Journal on Control and Optimization, Vol. 43, No. 3 | 26 July 2006AbstractPDF (213 KB)Design of Homogeneous Time-Varying Stabilizing Control Laws for Driftless Controllable Systems Via Oscillatory Approximation of Lie Brackets in Closed LoopSIAM Journal on Control and Optimization, Vol. 38, No. 1 | 26 July 2006AbstractPDF (506 KB)An Approximation Algorithm for Nonholonomic SystemsSIAM Journal on Control and Optimization, Vol. 35, No. 4 | 26 July 2006AbstractPDF (642 KB)Linearized Control Systems and Applications to Smooth StabilizationSIAM Journal on Control and Optimization, Vol. 32, No. 2 | 14 July 2006AbstractPDF (2245 KB)The Realization Problem for a Class of Nonlinear SystemsSIAM Journal on Matrix Analysis and Applications, Vol. 11, No. 1 | 17 July 2006AbstractPDF (982 KB)Strong Controllability of Nonlinear SystemsSIAM Journal on Control and Optimization, Vol. 24, No. 2 | 17 February 2012AbstractPDF (1419 KB)Recent Developments and Future Perspectives in Nonlinear System TheorySIAM Review, Vol. 24, No. 3 | 10 July 2006AbstractPDF (3427 KB)Invertibility of Nonlinear Control SystemsSIAM Journal on Control and Optimization, Vol. 17, No. 2 | 18 July 2006AbstractPDF (924 KB)Local Controllability and Sufficient Conditions in Singular Problems. IISIAM Journal on Control and Optimization, Vol. 14, No. 6 | 18 July 2006AbstractPDF (1555 KB)Global Controllability of Nonlinear SystemsSIAM Journal on Control and Optimization, Vol. 14, No. 4 | 18 July 2006AbstractPDF (1166 KB)Global Bilinearization of Systems with Control Appearing LinearlySIAM Journal on Control, Vol. 13, No. 4 | 18 July 2006AbstractPDF (511 KB)A Generalization of Chow's Theorem and the Bang-Bang Theorem to Nonlinear Control ProblemsSIAM Journal on Control, Vol. 12, No. 1 | 18 July 2006AbstractPDF (893 KB)Controllability of Nonlinear Systems on Compact ManifoldsSIAM Journal on Control, Vol. 12, No. 1 | 18 July 2006AbstractPDF (332 KB)On the Equivalence of Control Systems and the Linearization of Nonlinear SystemsSIAM Journal on Control, Vol. 11, No. 4 | 18 July 2006AbstractPDF (509 KB)Lie Theory and Control Systems Defined on SpheresSIAM Journal on Applied Mathematics, Vol. 25, No. 2 | 12 July 2006AbstractPDF (1172 KB)A Survey of Recent Results in Differential EquationsSIAM Review, Vol. 15, No. 2 | 2 August 2006AbstractPDF (1587 KB)The "Bang-Bang" Problem for Certain Control Systems in $GL(n,R)$SIAM Journal on Control, Vol. 10, No. 3 | 18 July 2006AbstractPDF (652 KB)System Theory on Group Manifolds and Coset SpacesSIAM Journal on Control, Vol. 10, No. 2 | 18 July 2006AbstractPDF (1759 KB)Global Controllability of Nonlinear SystemsSIAM Journal on Control, Vol. 10, No. 1 | 18 July 2006AbstractPDF (1137 KB)Contrôlabilité des Systèmes non LinéairesSIAM Journal on Control, Vol. 8, No. 4 | 18 July 2006AbstractPDF (64421 KB) Volume 8, Issue 4| 1970SIAM Journal on Control441-605 History Submitted:15 July 1969Accepted:15 March 1970Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0308033Article page range:pp. 450-460ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics