Abstract
Ritt’s algorithm can be used to compute a controller for a nonlinear system, so that the closed loop dynamics agrees with a specified differential polynomial. A necessary condition for a practical controller is that the system is minimum phase.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
C.I. Byrnes and A. Isidori, A frequency domain philosophy for nonlinear systems, with applications to stabilization and to adaptive control, Preprints of the 23rd IEEE Conference on Decision and Control, 1984, 1569–1573.
C. I. Byrnes and A. Isidori, Global feedback stabilization of nonlinear systems. Preprints of the 24:th IEEE Conference on Decision and Control, 1985, 1031–37.
P. E. Crouch, F. Lamnabhi — Lagarrigue, State space realizations of nonlinear systems defined by input — output differential equations. Proc. 8th Internat. Conf. Analysis and Optimization of Systems, Antibes, June 1988, A. Bensousan and J.L. Lions eds., Lect. Notes Control Inform. Sci., 111 (1988), 138–149, Springer, Berlin.
S. Diop, A state elimination procedure for nonlinear systems, in “New trends in Nonlinear Control Theory”, J. Descusse, M. Fliess, A. Isidori, D. Leborgne (eds.), Lect. Notes Control Inform. Sci. 122, pp 190–198, Springer, Berlin, 1989.
M. Fliess, A new approach to the structure at infinity of nonlinear systems, Systems and Control Letters 7, 1986, 419–421.
M. Fliess, A note on the invertibility of nonlinear input-output differential systems. Systems and Control Letters 8, 1987, 147–151.
M. Fliess, Quelques définitions de la théorie des systèmes à la lumière des corps différentiels, C. R. Acad. Sci. Paris, I-304, 1987, pp 91–93.
M. Fliess, Nonlineax control theory and differential algebra, in “Modelling and Adaptive Control”, Ch. I. Byrnes & A. Kurzhanski eds., Lect. Notes Control Inform. Sci. 105, pp 134–145, Springer, Berlin, 1988.
M. Fliess, Automatique et corps différentiels, Forum Math., 1, 1989, pp 227–238.
S.T. Glad, Nonlinear state space and input output descriptions using differential polynomials, in “New trends in Nonlinear Control Theory”, J. Descusse, M. Fliess, A. Isidori, D. Leborgne (eds.), Lect. Notes Control Inform. Sci. 122, pp 182–189, Springer, Berlin, 1989.
E.R. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973.
J. F. Ritt, Differential algebra, American Mathematical Society, Providence, RI, 1950.
A. J. van der Schaft, Transformation of nonlinear systems under external equivalence, in “New trends in Nonlinear Control Theory”, J. Descusse, M. Fliess, A. Isidori, D. Leborgne (eds.), Lect. Notes Control Inform. Sci. 122, pp 33–43, Springer, Berlin, 1989.
E. D. Sontag, Y. Wang, Input/output equations and realizability, MTNS-89, Amsterdam, 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Birkhäuser Boston
About this chapter
Cite this chapter
Glad, S.T. (1991). Nonlinear regulators and Ritt’s remainder algorithm. 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_19
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3214-8_19
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7835-1
Online ISBN: 978-1-4612-3214-8
eBook Packages: Springer Book Archive