Geodesic
Dynamic Equivalence of Control Systems and Infinite Permutation Matrices
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

To each dynamic equivalence of two control systems is associated an infinite permutation matrix. We investigate how such matrices are related to the existence of dynamic equivalences.
Keywords: dynamic equivalence, control systems. 
@article{SIGMA_2019_15_a62,
     author = {Jeanne N. Clelland and Yuhao Hu and Matthew W. Stackpole},
     title = {Dynamic {Equivalence} of {Control} {Systems} and {Infinite} {Permutation} {Matrices}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2019},
     volume = {15},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a62/}
}
TY  - JOUR
AU  - Jeanne N. Clelland
AU  - Yuhao Hu
AU  - Matthew W. Stackpole
TI  - Dynamic Equivalence of Control Systems and Infinite Permutation Matrices
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2019
VL  - 15
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a62/
LA  - en
ID  - SIGMA_2019_15_a62
ER  - 
%0 Journal Article
%A Jeanne N. Clelland
%A Yuhao Hu
%A Matthew W. Stackpole
%T Dynamic Equivalence of Control Systems and Infinite Permutation Matrices
%J Symmetry, integrability and geometry: methods and applications
%D 2019
%V 15
%U http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a62/
%G en
%F SIGMA_2019_15_a62
Jeanne N. Clelland; Yuhao Hu; Matthew W. Stackpole. Dynamic Equivalence of Control Systems and Infinite Permutation Matrices. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a62/

[1] Anderson R. L., Ibragimov N. H., Lie–Bäcklund transformations in applications, SIAM Studies in Applied Mathematics, 1, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa., 1979 | MR

[2] Aranda-Bricaire E., Moog C. H., Pomet J.-B., “Infinitesimal Brunovský form for nonlinear systems with applications to dynamic linearization”, Geometry in Nonlinear Control and Differential Inclusions (Warsaw, 1993), Banach Center Publ., 32, Polish Acad. Sci. Inst. Math., Warsaw, 1995, 19–33 | DOI | MR | Zbl

[3] Bryant R. L., Chern S. S., Gardner R. B., Goldschmidt H. L., Griffiths P. A., Exterior differential systems, Mathematical Sciences Research Institute Publications, 18, Springer-Verlag, New York, 1991 | DOI | MR | Zbl

[4] Cartan E., “Sur l'équivalence absolue de certains systèmes d'équations différentielles et sur certaines familles de courbes”, Bull. Soc. Math. France, 42 (1914), 12–48 | DOI | MR

[5] Chetverikov V. N., “Invertible linear ordinary differential operators”, J. Geom. Phys., 113 (2017), 10–27 | DOI | MR | Zbl

[6] Fliess M., Lévine J., Martin P., Rouchon P., “A Lie–Bäcklund approach to equivalence and flatness of nonlinear systems”, IEEE Trans. Automat. Control, 44 (1999), 922–937 | DOI | MR | Zbl

[7] Jakubczyk B., “Equivalence of differential equations and differential algebras”, Tatra Mt. Math. Publ., 4 (1994), 125–130 | MR | Zbl

[8] Krasil'shchik I. S., Lychagin V. V., Vinogradov A. M., Geometry of jet spaces and nonlinear partial differential equations, Advanced Studies in Contemporary Mathematics, 1, Gordon and Breach Science Publishers, New York, 1986 | MR | Zbl

[9] Lévine J., “On necessary and sufficient conditions for differential flatness”, Appl. Algebra Engrg. Comm. Comput., 22 (2011), 47–90, arXiv: math.OC/0605405 | DOI | MR | Zbl

[10] Martin P., Murray R. M., Rouchon P., “Flat systems, equivalence and feedback”, Advances in the Control of Nonlinear Systems (Murcia, 2000), Lect. Notes Control Inf. Sci., 264, Springer, London, 2001, 5–32 | DOI | MR

[11] Nicolau F., Respondek W., “Flatness of multi-input control-affine systems linearizable via one-fold prolongation”, SIAM J. Control Optim., 55 (2017), 3171–3203 | DOI | MR | Zbl

[12] Pomet J.-B., “A differential geometric setting for dynamic equivalence and dynamic linearization”, Geometry in Nonlinear Control and Differential Inclusions (Warsaw, 1993), Banach Center Publ., 32, Polish Acad. Sci. Inst. Math., Warsaw, 1995, 319–339 | DOI | MR | Zbl

[13] Sluis W. M., Absolute equivalence and its applications to control theory, Ph.D. Thesis, University of Waterloo, 1992 | MR

[14] Stackpole M. W., “Dynamic equivalence of control systems via infinite prolongation”, Asian J. Math., 17 (2013), 653–688, arXiv: 1106.5437 | DOI | MR | Zbl