@article{AIHPA_1997__66_3_275_0,
author = {Fliess, Michel and L\'evine, Jean and Martin, Philippe and Rouchon, Pierre},
title = {Deux applications de la g\'eom\'etrie locale des diffi\'et\'es},
journal = {Annales de l'I.H.P. Physique th\'eorique},
pages = {275--292},
year = {1997},
publisher = {Gauthier-Villars},
volume = {66},
number = {3},
mrnumber = {1456514},
zbl = {0895.58003},
language = {fr},
url = {https://www.numdam.org/item/AIHPA_1997__66_3_275_0/}
}
TY - JOUR AU - Fliess, Michel AU - Lévine, Jean AU - Martin, Philippe AU - Rouchon, Pierre TI - Deux applications de la géométrie locale des diffiétés JO - Annales de l'I.H.P. Physique théorique PY - 1997 SP - 275 EP - 292 VL - 66 IS - 3 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPA_1997__66_3_275_0/ LA - fr ID - AIHPA_1997__66_3_275_0 ER -
%0 Journal Article %A Fliess, Michel %A Lévine, Jean %A Martin, Philippe %A Rouchon, Pierre %T Deux applications de la géométrie locale des diffiétés %J Annales de l'I.H.P. Physique théorique %D 1997 %P 275-292 %V 66 %N 3 %I Gauthier-Villars %U https://www.numdam.org/item/AIHPA_1997__66_3_275_0/ %G fr %F AIHPA_1997__66_3_275_0
Fliess, Michel; Lévine, Jean; Martin, Philippe; Rouchon, Pierre. Deux applications de la géométrie locale des diffiétés. Annales de l'I.H.P. Physique théorique, Tome 66 (1997) no. 3, pp. 275-292. https://www.numdam.org/item/AIHPA_1997__66_3_275_0/
[1] , et , Geometry I, Basic Ideas and Concepts of Differential Geometry, Encycl. Math. Sci., Vol. 28, Springer-Verlag, Berlin, 1991. | MR
[2] et , Lie-Bäcklund Transformations in Applications, S.I.A.M., Philadelphie, 1979. | Zbl
[3] , Traité de Mécanique Rationnelle, t. 2, 6e éd., Gauthier-Villars, Paris, 1953.
[4] , et , Mathematical Aspects of Classical and Celestial Mechanics, in Dynamical Systems III, Encycl. Math. Sci., Vol. 3, Springer-Verlag, Berlin, 1988. | MR
[5] , Rings of Differential Operators, North-Holland, Amsterdam, 1979. | Zbl | MR
[6] , et , Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Elsevier, Amsterdam, 1989. | Zbl | MR
[7] , Differential Algebraic Groups of Finite Dimension, Springer-Verlag, Berlin, 1992. | Zbl | MR
[8] , Differential Algebra and Diophantine Geometry, Hermann, Paris, 1994. | Zbl | MR
[9] , The classification of the semisimple differential algebraic groups and the linear semisimple differential algebraic Lie algebras, J. Algebra, Vol. 121, 1989, p. 169-238. | Zbl | MR
[10] , Free Rings and their Relations, 2nd ed., Academic Press, Londres, 1985.
[11] , Mécanique hamiltonienne en présence de contraintes, Illinois J. Math., Vol. 38, 1994, p. 148-175. | Zbl | MR
[12] et , Lowering the orders of derivatives of controls in generalized state space systems, J. Math. Systems Estimat. Control, Vol. 5, 1995, p. 375-378. | Zbl | MR
[13] , Soliton Equations and Hamiltonian Systems, World Scientific, Singapour, 1991. | Zbl | MR
[14] , Dirac Structures and Integrability of Nonlinear Evolution Equations, Wiley, Chichester, 1993. | MR
[15] , Automatique et corps différentiels, Forum Math., Vol. 1, 1989, p. 227-238. | Zbl | MR
[16] , Generalized controller canonical forms for linear and nonlinear dynamics, IEEE Trans. Automat. Control, Vol. 35, 1990, p. 994-1001. | Zbl | MR
[17] and , An algebraic approach to linear and nonlinear control, in Essays on Control: Perspectives in the Theory and its Applications (H. Trentelman and J. C. Willems Eds), Birkhäuser, Boston, 1993, p. 223-267. | Zbl | MR
[18] , , , et , Flatness and dynamic feedback linearizability: two approaches, Proc. 3rd European Control Conf., Rome, 1995, p. 649-654.
[19] , , et , Linéarisation par bouclage dynamique et transformations de Lie-Bäcklund, C. R. Acad. Sci. Paris, Vol. I-317, 1993, p. 981-986. | Zbl | MR
[20] , , et , Nonlinear control and Lie-Bäcklund transformations: Towards a new differential geometric standpoint, Proc. IEEE Control Decision Conf., Lake Buena Vista, FL, 1994, p. 339-344.
[21] , , et , Flatness and defect of non-linear systems: introductory theory and examples, Internat. J. Control, Vol. 61, 1995, p. 1327-1361. | Zbl | MR
[22] , , et , Index and decomposition of nonlinear implicit differential equations, Proc. IFAC Conf. System Structure Control, Nantes, 1995, p. 43-48.
[23] , , et , Design of trajectory stabilizing feedback for driftless flat systems, Proc. 3rd European Control Conf., Rome, 1995, p. 1882-1887.
[24] , , et , A Lie-Bäcklund transformation approach to equivalence and flatness of nonlinear systems, à paraître.
[25] , et , A generalised state variable representation for a simplified crane description, Internat. J. Control, Vol. 58, 1993, p. 277-283. | Zbl | MR
[26] , Jet methods in nonholonomic mechanics, J. Math. Physics, Vol. 33, 1992, p. 1652-1665. | Zbl | MR
[27] , Partial Differential Relations, Springer-Verlag, Berlin, 1986. | Zbl | MR
[28] , et , Secondary differential operators, J. Geometry Physics, Vol. 2, 1985, p. 23-65. | Zbl | MR
[29] , et , The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Springer-Verlag, Berlin, 1989. | Zbl | MR
[30] , Theoretische Mechanik, Springer-Verlag, Berlin, 1949. | MR
[31] , Algebraic Geometry, Springer-Verlag, New York, 1977. | Zbl | MR
[32] et , Quantization of Gauge Systems, Princeton University Press, Princeton, 1992. | Zbl | MR
[33] , Transformation Groups Applied to Mathematical Physics, Reidel, Boston, 1985. | Zbl
[34] , Nonlinear Control Systems, 3rd ed., Springer-Verlag, New York, 1995.
[35] , Kähler differentials and differential algebra, Ann. of Math., Vol. 89, 1969, p. 92-98. | Zbl | MR
[36] , Prolongations of integral domains, J. Algebra, Vol. 94, 1985, p. 173-211. | MR
[37] , Differential Algebra and Algebraic Groups, Academic Press, New York, 1973. | Zbl | MR
[38] , Differential Algebraic Groups, Academic Press, Orlando, 1985. | Zbl | MR
[39] , et , Geometry of Jet Spaces and Nonlinear Partial Differential Equations, Gordon and Breach, New York, 1986. | Zbl | MR
[40] , The Variational Principles of Dynamics, World Scientific, Singapour, 1992. | Zbl | MR
[41] , Algebraic aspects of nonlinear differential equations, J. Soviet Math., Vol. 11, 1979, p. 1-122. | Zbl
[42] et , Classical dynamics of non-holonomic systems, Ann. Inst. H. Poincaré Phys. Théor., Vol. 55, 1991, p. 511-544. | Zbl | MR | Numdam
[43] et , Jet bundle geometry, dynamical connections, and the inverse problem of Lagrangian mechanics, Ann. Inst. H. Poincaré Phys. Théor., Vol. 61, 1994, p. 17-62. | Zbl | MR | Numdam
[44] et , Dynamics of Nonholonomic Systems, Amer. Math. Soc., Providence, R.I., 1972.
[45] et , Nonlinear Control Systems, Springer-Verlag, New York, 1990. | Zbl
[46] , Applications of Lie Groups to Differential Equations, 2nd ed., Springer-Verlag, New York, 1993. | Zbl | MR
[47] , Differential Algebra, Amer. Math. Soc., New York, 1950. | Zbl
[48] , Idéaux de Fonctions Différentiables, Springer-Verlag, Berlin, 1972. | Zbl | MR
[49] , Formal geometry of systems of differential equations, Sugaku Expos., Vol. 3, 1990, p. 25-73. | Zbl
[50] , Homological method of computing invariants of systems of differential equations, Diff. Geometry Appl., Vol. 1, 1991, p. 3-34. | Zbl | MR
[51] , Local symmetries and conservation laws, Acta Appl. Math., Vol. 2, 1984, p. 21-78. | Zbl | MR
[52] , Ed., Symmetries of Partial Differential Equations, Kluwer, Dordrecht, 1989 (reprinted from Acta Appl. Math., Vol. 15, 1989, n° 1-2, and Vol. 16, 1989, n° 1-2). | Zbl | MR
[53] , Scalar differential invariants, diffieties and characteristic classes, in Mechanics, Analysis and Geometry: 200 Years after Lagrange (M. Francaviglia Ed.), North-Holland, Amsterdam, 1991, p. 379-416. | Zbl | MR
[54] , From symmetries of partial differential equations towards secondary ("quantized") calculus, J. Geometry Physics, Vol. 14, 1994, p. 146-194. | Zbl | MR
[55] , A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 4th ed., Cambridge University Press, Cambridge, 1947. | MR
[56] , On Bäcklund correspondences, Math. USSR Sb., Vol. 64, 1989, p. 277-293. | Zbl | MR
[57] , Geometrical Aspects of Partial Differential Equations, World Scientific, Singapour, 1992. | Zbl | MR






