Nous présentons dans cette Note une forme normale pour les sytèmes de contrôle non linéaires mono-sortie. Nous suivons une approche proposée par Poincaré et adaptée aux systèmes de contrôle par Kang et Krener, consistant à analyser, pas-à-pas, l'action du changement de coordonnées sur le système.
We propose a normal form for nonlinear control systems with scalar output. We follow an approach proposed by Poincaré and adapted for control systems by Kang and Krener which consists of analyzing, step-by-step, the action of the change of coordinates on the system.
Accepté le :
Publié le :
@article{CRMATH_2005__341_9_573_0, author = {Tall, Issa A. and Balde, Moussa}, title = {Normal forms for nonlinear control systems with scalar output}, journal = {Comptes Rendus. Math\'ematique}, pages = {573--578}, publisher = {Elsevier}, volume = {341}, number = {9}, year = {2005}, doi = {10.1016/j.crma.2005.09.023}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.09.023/} }
TY - JOUR AU - Tall, Issa A. AU - Balde, Moussa TI - Normal forms for nonlinear control systems with scalar output JO - Comptes Rendus. Mathématique PY - 2005 SP - 573 EP - 578 VL - 341 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.09.023/ DO - 10.1016/j.crma.2005.09.023 LA - en ID - CRMATH_2005__341_9_573_0 ER -
%0 Journal Article %A Tall, Issa A. %A Balde, Moussa %T Normal forms for nonlinear control systems with scalar output %J Comptes Rendus. Mathématique %D 2005 %P 573-578 %V 341 %N 9 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.09.023/ %R 10.1016/j.crma.2005.09.023 %G en %F CRMATH_2005__341_9_573_0
Tall, Issa A.; Balde, Moussa. Normal forms for nonlinear control systems with scalar output. Comptes Rendus. Mathématique, Tome 341 (2005) no. 9, pp. 573-578. doi : 10.1016/j.crma.2005.09.023. http://archive.numdam.org/articles/10.1016/j.crma.2005.09.023/
[1] Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, Berlin/New York, 1983
[2] I. Belmouhoub, M. Diemaï, J.P. Barbot, Observability quadratic normal form for discrete-time systems, Preprint
[3] L. Boutat, D. Boutat, J.P. Barbot, R. Tauleigne, Quadratic observability normal form, in: Proc. of the 40th IEEE Conf. on Decision & Control, Orlando, FL, 2001
[4] Extended controller form and invariants of nonlinear control systems with single input, J. Math. Systems Estimat. Control, Volume 4 (1994), pp. 253-256
[5] Locally convergent nonlinear observers, SIAM J. Control Optim., Volume 42 (2003) no. 1, pp. 155-177
[6] Extended quadratic controller normal form and dynamic feedback linearization of nonlinear systems, SIAM J. Control Optim., Volume 30 (1992), pp. 1319-1337
[7] Linearization by output injection and nonlinear observers, Systems Control Lett., Volume 3 (1983), pp. 47-52
[8] Nonlinear observers with linearizable error dynamics, SIAM J. Control, Optim., Volume 23 (1985) no. 2
[9] Sur les propriétés des fonctions définies par les équations aux différences partielles, Oeuvres, Gauthier-Villars, Paris, 1929 (pp. XCIX–CX)
[10] Nonlinearizable single-input control systems do not admit stationary symmetries, Systems Control Lett., Volume 46 (2002), pp. 1-16
[11] W. Respondek, I.A. Tall, Strict feedforward form and symmetries of nonlinear control systems, in: Proc. of the 43rd IEEE Conf. on Decision and Control, Bahamas, 2004
Cité par Sources :