Nonlinear Controllability via Lie Theory

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 SectionsAbout1 Wei-Liang Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Math. Ann. , 117 (1939), 98–105 10. 1007/BF01450011 MR0001880 0022. 02304 CrossrefGoogle Scholar2 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 Scholar3 Robert Hermann, The differential geometry of foliations. II, J. Math. Mech. , 11 (1962), 303–315 MR0142131 0152. 20502 ISIGoogle Scholar4 Robert Hermann, Some differential-geometric aspects of the Lagrange variational problem, Illinois J. Math. , 6 (1962), 634–673 MR0145457 0196. 54301 CrossrefGoogle Scholar5 Jan Kučera, Solution in large of control problem x= (Au+Bv) x, Czechoslovak Math. J. , 17 (92) (1967), 91–96 MR0226103 0189. 15701 ISIGoogle Scholar6 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