Résumé
Nous proposons dans les cas linéaire ou non des formules explicites pour calculer le rang différentiel de sortie. Nous utilisons une généralisation à l’algèbre différentielle des polynômes de Hilbert-Serre, classiques en théorie de la dimension, due à E.R. Kolchin et J. Johnson. Nous comparons nos résultats à diverses approches précédentes.
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References
N. Bourbaki, “Algèbre commutative”, Chap. 3, Graduations, Filtrations et Topologies, Masson, Paris, 1985.
N. Bourbaki, “Algèbre”, chap. 4 à 7, Masson, Paris, 1981.
J. Descusse, C. H. Moog, “Dynamic decoupling for right-invertible nonlinear systems”, Syst. Contr. Lett., 8, p. 345–349, 1987.
M. D. Di Benedetto, J. W. Grizzle, C.H. Moog, “Rank invariants of nonlinear systems”, SIAM J. Control Optim. 27, p. 658–672, 1989.
M. Fliess, “Automatique et corps différentiels”, Forum Math., 1, p. 227–238, 1989.
M. Fliess, “Generalized linear systems with lumped or distributed parameters”, Int. J. Control, 49, p. 1989–1999, 1989.
M. Fliess, “Some basic structural properties of generalized linear systems”, Syst. Contr. Lett., 15, 1990, n° 5.
A. Glumineau et C. H. Moog, “Essential orders and the nonlinear decoupling problem”, Int. J. Control, 50, p. 1825–1834, 1989.
K.A. Grasse, “Sufficient conditions for the functional reproducibility of time-varying, input-output systems”, SIAM J. Control Optim., 26, p. 230–249, 1988.
R. M. Hirschorn, “Invertibility of multivariable nonlinear systems”, IEEE Trans. Automat. Control, 24, p. 855–865, 1979.
H. J. C. Huijberts, H. Nijmeijer, L. L. M. Van der Wegen, “Dynamic disturbance decoupling for nonlinear systems”, à paraître.
J. Johnson, “Differential dimension polynomials and a fundamental theorem on differential modules”, Amer. J. Math., 91, p. 239–248, 1969.
J. Johnson, “Kähler differentials and differential algebra”, Ann. Math., 89, p, 92–98, 1969.
E. R. Kolchin, “Differential Algebra and Algebraic groups”, Academic Press, New York, 1973.
H. Nijmeijer, “Right-invertibility for a class of nonlinear control systems: geometric approach, System Control Lett, 7, p. 125–132, 1986.
P. Rouchon, “Simulation dynamique et commande nonlinéaire des colonnes à distiller”, Thèse, Ecole Nationale Supérieure des Mines de Paris, 1990.
M. K. Sain et J. L. Massey, “Invertibility of linear time-invariant dynamic systems”, IEEE Trans. Automat. Contol, AC-14, p. 141–149, 1969.
L. M. Silverman, “Inversion of multivariable linear system”, IEEE Trans. Automat. Control, AC-14, p. 141–149, 1969.
S. N. Singh, “A modified algorithm for invertibility in nonlinear systems”. IEEE Trans. Automat. Control, AC-26, p. 595–598, 1981.
M. Vukobratovic, R. Stojic, “Modern aircraft flight control”, Lecture Notes in Control and Information Sciences, Springer-Verlag, Vol 109, 1988.
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© 1991 Birkhäuser Boston
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El Asmi, S., Fliess, M. (1991). Formules d’inversion. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_17
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DOI: https://doi.org/10.1007/978-1-4612-3214-8_17
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