×

zbMATH — the first resource for mathematics

Construction of a controller with a generalized linear immersion. (English) Zbl 1236.93044
Summary: Gröbner bases for modules are used to calculate a generalized linear immersion for a plant whose solutions to its regulation equations are polynomials or pseudo-polynomials. After calculating the generalized linear immersion, we build the controller which gives the robust regulation.
MSC:
93B35 Sensitivity (robustness)
93C10 Nonlinear systems in control theory
93D15 Stabilization of systems by feedback
13E05 Commutative Noetherian rings and modules
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
Software:
SINGULAR
PDF BibTeX XML Cite
Full Text: Link EuDML
References:
[1] Atiyah, M. F., MacDonald, I. G.: Introduction to Commutative Algebra. Addison-Wesley Publishing Company, Inc., Reading, Massachusetts 1969. · Zbl 0175.03601
[2] Byrnes, C. I., Isidori, A.: Output regulation for nonlinear systems: an overview. Internat. J. Robust Nonlinear Control 10 (2000), 323-337. <a href=”http://dx.doi.org/10.1002/(SICI)1099-1239(20000430)10:53.0.CO;2-G” target=”_blank”>DOI 10.1002/(SICI)1099-1239(20000430)10:53.0.CO;2-G | · Zbl 0962.93007
[3] Castillo-Toledo, B., Čelikovský, S., Gennaro, S. Di: Generalized immersion and nonlinear robust output regulation problem. Kybernetika 40 (2004), 207-220. · Zbl 1249.93055
[4] Chen, Z., Huang, J.: A general formulation and sovability of the global output regulation problem. Proc. 42nd IEEE Conf. on Decision & Control, Mawui 2003, pp. 1071-1079.
[5] Francis, B. A., Wonham, W. M.: The internal model principle of control theory. Automatica J. IFAC 12 (1976), 457-465. · Zbl 0344.93028
[6] Greuel, G.-M., Pfister, G.: A Singular Introduction to Commutative Algebra. Springer-Verlag, Berlin 2002. · Zbl 1023.13001
[7] Isidori, A.: Nonlinear Control Systems. Third edition. Springer-Verlag, Berlin 1995. · Zbl 0878.93001
[8] Isidori, A., Byrnes, C. I.: Output regulation of nonlinear systems. IEEE Trans. Automat. Control 35 (1990), 131-140. · Zbl 0704.93034
[9] Knobloch, H.-W., Isidori, A., Flockerzi, D.: Topics in Control Theory. Birkhäuser Verlag, Basel 1993. · Zbl 0789.93073
[10] Mora, F.: An algorithm to compute the equations of tangents cones. Proc. EUROCAM 82, Lecture Notes In Comput. Sci. 144, Springer, Berlin-New - York 1982, pp. 158-165.
[11] Ogata, K.: Modern Control Engineering. Third edition. Prentice-Hall, Upper Saddle River, New Jersey 1997. · Zbl 0756.93060
[12] Tuyub-Puc, D. R.: Aplicación de las Bases de Gröbner a la construcción de un controlador con una Inmersión Lineal Generalizada. Master’s thesis. Universidad Autónoma de Yucatán 2009.
[13] Villanueva-Novelo, C., Čelikovský, S., Castillo-Toledo, B.: Structurally stable design of output regulation for a class of nonlinear systems. Kybernetika 37 (2001), 547-564. · Zbl 1265.93218
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.