A remark on nonlinear accessibility conditions and infinite prolongations

Systems and Control Letters - Tập 31 - Trang 77-83 - 1997
Michel Fliess1, Jean Lévine2, Philippe Martin2, François Ollivier3, Pierre Rouchon4
1Laboratoire des Signaux et Systèmes, CNRS-Supélec, Plateau de Moulon, 91192 Gif-sur-Yvette, France
2Centre Automatique et Systèmes, École des Mines de Paris, 35 rue Saint-Honoré, 77305 Fontainebleau, France
3GAGE-CNRS, Centre de Mathématiques, École Polytechnique, 91128 Palaiseau, France
4Centre Automatique et Systèmes, École des Mines de Paris, 60 bld. Saint-Michel, 75272 Paris Cedex 06, France

Tài liệu tham khảo

Abbott, 1996 Abraham, 1988 Alekseevskij, 1991, Geometry I, Basic Ideas and Concepts from Differential Geometry, vol. 28 Anderson, 1979 Aranda-Bricaire, 1995, A linear algebraic framework for dynamic feedback linearization, IEEE Trans. Automat. Control, 40, 127, 10.1109/9.362886 Bianchini, 1993, Controllability along a trajectory: A variational approach, SIAM J. Control Optim., 31, 900, 10.1137/0331039 Brockett, 1972, System theory on group manifolds and coset spaces, SIAM J. Control, 10, 265, 10.1137/0310021 Campbell, 1995, High index differential algebraic equations, J. Mech. Struct. Machines, 23, 199, 10.1080/08905459508905235 Charlet, 1991, Sufficient conditions for dynamic state feedback linearization, SIAM J. Control Optim., 29, 38, 10.1137/0329002 Delaleau, 1993, Sur la dérivée de l'entrée en représentation et commande des systèmes non linéaires Delaleau, 1992, Algorithme de structure, filtrations et découplage, C.R. Acad. Sci. Paris, I-315, 101 Delaleau, 1994, Conditions de rang pour le rejet dynamique de perturbations, C.R. Acad. Sci. Paris, I-319, 1121 E. Delaleau, P.S. Pereira da Silva, Filtrations in feedback synthesis, to appear in: Forum Math. Descusse, 1985, Decoupling with dynamic compensation for strong invertible affine non-linear control systems, Internat. J. Control, 42, 1387, 10.1080/00207178508933432 Descusse, 1987, Dynamic decoupling for right invertible nonlinear systems, Systems Control Lett., 8, 345, 10.1016/0167-6911(87)90101-0 DiBenedetto, 1989, Rank invariants of nonlinear systems, SIAM J. Control Optim., 27, 658, 10.1137/0327035 Diop, 1991, On nonlinear observability, 152 Elliott, 1970, A consequence of controllability, J. Differential Equations, 10, 364, 10.1016/0022-0396(71)90059-3 Fliess, 1989, Automatique et corps différentiels, Forum Math., 1, 227, 10.1515/form.1989.1.227 Fliess, 1990, Generalized controller canonical forms for linear and nonlinear dynamics, IEEE Trans. Automat. Control, 35, 994, 10.1109/9.58527 Fliess, 1992, A remark on Willems' trajectory characterization of linear controllability, Systems Control Lett., 19, 43, 10.1016/0167-6911(92)90038-T Fleiss, 1993, An algebraic approach to linear and nonlinear control, 223 Fliess, 1997, Controlling nonlinear systems by flatness, 137 Fliess, 1993, Linéarisation par bouclage dynamique et transformations de Lie-Bäcklund, C.R. Acad. Sci. Paris, I-317, 981 Fliess, 1994, Nonlinear control and Lie-Bäcklund transformations: Towards a new differential geometric standpoint, 981 Fliess, 1995, Flatness and defect of nonlinear systems: Introductory theory and applications, Internat. J. Control, 61, 1327, 10.1080/00207179508921959 Fliess, 1995, Design of trajectory stabilizing feedback for driftless flat systems, 1882 Fliess, 1996, A Lie-Bäcklund approach to dynamic feedback equivalence and flatness, vol. 217, 245 Fliess, 1997, Deux applications de la géométrie locale des diffiétés, Ann. Inst. H. Poincaré Phys. Théor., 66 Fliess, 1993, A generalised state variable representation for a simplified crane description, Internat. J. Control, 58, 277, 10.1080/00207179308923002 Fliess, 1997, Corps de Hardy et observateurs asymptotiques locaux pour systèmes différentiellement plats, C.R. Acad. Sci. Paris, II-324 Golubitsky, 1973 Haynes, 1970, Nonlinear controllability via Lie theory, SIAM J. Control, 8, 450, 10.1137/0308033 Hermann, 1963, On the accessibility problem in control theory, 325 Hermann, 1977, Nonlinear controllability and observability, IEEE Trans. Automat. Control, 22, 728, 10.1109/TAC.1977.1101601 Huijberts, 1992, A nonregular solution of the nonlinear dynamic disturbance decoupling problem with an application to a complete solution of the nonlinear model matching problem, SIAM J. Control Optim., 30, 350, 10.1137/0330022 Huijberts, 1992, Dynamic disturbance decoupling for nonlinear systems, SIAM J. Control Optim., 30, 336, 10.1137/0330021 Ibragimov, 1985 Isidori, 1995 Kawski, 1990, High order small time local controllability, 431 Krasil'shchik, 1986 Krener, 1974, A generalization of Chow's theorem and the bang-bang theorem to nonlinear control systems, SIAM J. Control, 12, 43, 10.1137/0312005 Lobry, 1970, Contrôlabilité des systèmes non linéaires, SIAM J. Control, 8, 573, 10.1137/0308042 McLellan, 1994, A differential-algebraic perspective on nonlinear controller design methodologies, Chem. Eng. Sci., 49, 1663, 10.1016/0009-2509(93)E0012-2 Moog, 1988, Nonlinear decoupling and structure at infinity, Math. Control Signal Systems, 1, 257, 10.1007/BF02551287 Nijmeijer, 1988, Dynamic input-output decoupling of nonlinear control systems, IEEE Trans. Automat. Control, 33, 1065, 10.1109/9.14420 Nijmeijer, 1990 van Nieuwstadt, 1994, Differential flatness and absolute equivalence, 326 Olver, 1993 Olver, 1995 Pereira da Silva, 1996, On the nonlinear dynamic disturbance decoupling problem, J. Math. Systems Estim. Control, 6, 1 Pomet, 1995, A differential geometric setting for dynamic equivalence and dynamic linearization, 319 Respondek, 1990, Right and left invertibility of nonlinear control systems, 133 Rudolph, 1994, Viewing input-output system equivalence from differential algebra, J. Math. Systems Estim. Control, 4, 353 Rudolph, 1995, Well-formed dynamics under quasi-static state feedback, 349 J. Rudolph, E. Delaleau, Some examples and remarks on quasi-static feedback of generalized states, to appear in: Automatica. van der Schaft, 1982, Observability and controllability for smooth nonlinear systems, SIAM J. Control Optim., 20, 338, 10.1137/0320026 Singh, 1981, A modified algorithm for invertibility in nonlinear systems, IEEE Trans. Automat. Control, 26, 595, 10.1109/TAC.1981.1102657 Sluis, 1993, A necessary condition for dynamic feedback linearization, Systems Control Lett., 21, 277, 10.1016/0167-6911(93)90069-I Sluis, 1996, A bound on the number of integrators needed to linearize a control systems, Systems Control Lett., 29, 43, 10.1016/0167-6911(96)00046-1 Sussmann, 1973, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc., 180, 171, 10.1090/S0002-9947-1973-0321133-2 Sussmann, 1983, Lie brackets, real analyticity and geometric control, 1 Sussmann, 1987, A general theorem on local controllability, SIAM J. Control Optim., 25, 158, 10.1137/0325011 Sussmann, 1972, Controllability of nonlinear systems, J. Differential Equations, 12, 95, 10.1016/0022-0396(72)90007-1 Tsujishita, 1990, Formal geometry of systems of differential equations, Sugaky Expos., 3, 25 Vinogradov, 1984, Local symmetries and conservation laws, Acta Appl. Math., 2, 21, 10.1007/BF01405491 1989 1989, 15 1989, 16 Willems, 1992, Paradigms and puzzles in the theory of dynamical systems, IEEE Trans. Automat. Control, 36, 259, 10.1109/9.73561 Zharinov, 1992