En este artículo se describe la aplicación, a sistemas discontinuos o multivaluados, de una metodología de diseño de observadores basada en la disipatividad, por medio del uso de la teoría de inclusiones diferenciales y de una generalización del teorema del círculo. Los sistemas susceptibles de ser tratados por medio de este método son aquellos que pueden ser expresados en la forma de Lur’e, y en los que se permite la inclusión de no linealidades discontinuas o multivaluadas, y en general no Lipschitz. El método presentado elimina restricciones que otros métodos imponen en cuanto a la monotonía y la igualdad de número de entradas y salidas de las no linealidades permitidas.
Información de la revista
Vol. 5. Núm. 1.
Páginas 27-36 (enero 2008)
Vol. 5. Núm. 1.
Páginas 27-36 (enero 2008)
Open Access
Diseño disipativo de observadores para sistemas no lineales discontinuos o multivaluados
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* Universidad Pontificia Bolivariana (UPB), Escuela de Ingeniería, Grupo de Investigación en Automática y Diseño. Cir 1 Num. 70-01. Medellín, Colombia
** Universidad Nacional Autónoma de México (UNAM), Automatización, Instituto de Ingeniería, Edificio 12, Circuito Exterior, 04510 México D.F., México. Tel: +52-55-56233600 ext. 8811
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Resumen
Palabras clave:
Sistemas no lineales
Observadores no lineales
Disipatividad
Mapeos Discontinuos
Mapeos Multivaluados
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Referencias
[Alessandri and Coletta., 2003]
A. Alessandri, P. Coletta.
Design of observers for switched discrete time linear systems.
Proceedings of the American Control Conference, (2003), pp. 2785-2790
[Alessandri and Baglietto, 2007]
A. Alessandri, M. Baglietto, G. Battistelli.
Design of observers with commutation-dependent gains for linear switching systems.
Proceedings of American Control Conference, (2007), pp. 2090-2095
[Arcak, 2001]
M. Arcak, P. Kokotovic.
Nonlinear observers: a circle criterion design and robustness analysis.
Automatica, 37 (2001), pp. 1923-1930
[Aubin, 1984]
J.P. Aubin, A. Cellina.
Differential Inclusions; Set-Valued Maps and Viability Theory.
Springer-Verlag, (1984),
[Bacciotti, 2001]
A. Bacciotti, L. Rosier.
Springer-Verlag, (2001),
[Boizot and Busvelle, 2007]
Boizot, N. and E. Busvelle (2007). Nonlinear Observers and Applications. Chap. Adaptive-Gain Observers and Applications, pp. 71-112. Number 363 In: Lecture Notes in Control and Information Sciences. Springer.
[Davila et al., 2005]
J. Davila, L. Fridman, A. Levant.
Second-order sliding-modes observer for mechanical systems.
IEEE Transactions on Automatic Control, 50 (2005), pp. 1785-1789
[Davila et al., 2006]
J. Davila, L. Fridman, A. Poznyak.
Observation and identification of mechanical systems via second order sliding modes.
International Journal of Control, 79 (2006), pp. 1251-1262
[Deimling, 1992]
K. Deimling.
Multivalued Differential Equations.
Gruyer, (1992),
[Dontchev and Lempio, 1992]
A. Dontchev, F. Lempio.
Difference methods for differential inclusions: A survey.
SIAM Review, 34 (1992), pp. 263-294
[Drakunov and Utkin, 1995]
S.V. Drakunov, V.I. Utkin.
Slidingmode observers tutorials.
Proceedings of 34 Conference on Decision and Control,
[Filippov, 1988]
A.F. Filippov.
Differential Equations with Discontinuous Righthand side.
Mathematics and its Applications (Soviet Series). Kluwer. Dordrecht, (1988),
[Gauthier et al., 1992]
J.P. Gauthier, H. Hammouri, S. Othman.
A simple observer for nonlinear systems. Applications to bioreactors.
IEEE Trans. Automatic Control, 37 (1992), pp. 875-880
[Haskara et al., 1998]
I. Haskara, Ü. Özgünner, V. Utkin.
On sliding mode observers via equivalent control approach.
International Journal of Control, 71 (1998), pp. 1051-1067
[Heemels et al., 2005]
W.P. Heemels, A.L. Juloski, B. Brogliato.
Observer design for lur’e systems with monotonic multivalued mappings.
Preprints of the 16th IFAC World Congress (IFAC, Ed.),
[Hill and Moylan, 1980]
D.J. Hill, P.J. Moylan.
Dissipative dynamical systems: Basic input-output and state properties.
Journal of the Franklin Institute, 309 (1980), pp. 327-357
[Juloski, 2004]
Juloski, A. L. (2004). Observer Design and Identification Methods for Hybrid Systems: Theory and Experiments. PhD thesis. Eindhoven University of Thechnology.
[Juloski et al., 2006]
A. Juloski, N. Mihajlovic, W. Heemels, N. Van de Wouw, H. Ñijmeijer.
Observer design for an experimental rotor system with discontinuous friction.
Proceedings of the 2006 American Control Conference, pp. 2886-2891
[Juloski et al., 2002]
A. Juloski, W. Heemels, S. Weiland.
Observer design for a class of piece-wise affine systems.
Proceedings of the Conference on Decision and Control, pp. 2606-2611
[Juloski et al., 2007]
A. Juloski, W. Heemels, S. Weiland.
Observer design for a class of piecewise linear systems.
Int. J. Robust Nonlinear Control, 17 (2007), pp. 1387-1404
[Khalil, 1999]
Khalil, H. K. (1999). High-gain observers in nonlinear feedback control. In: New Directions in Nonlinear Observer Design (H. Ñijmeijer and T.I. Fossen, Eds.). pp. 249–268. Number 244 In: Lecture notes in control and information sciences. Springer–Verlag. London.
[Khalil, 2002]
H.K. Khalil.
Nonlinear Systems.
3rd., Prentice-Hall. Upsaddle River, (2002),
[Moreno, 2004]
J.A. Moreno.
Observer design for nonlinear systems: A dissipative approach.
Proceedings of the 2nd IFAC Symposium on System, Structure and Control SSSC2004, pp. 735-740
[Moreno, 2005]
Moreno, J. A. (2005). Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems. Chap. Aproximate Observer Error Linearizaton by Dissipativity Methods, pp. 35–51. Number 322 In: Lecture Notes in Control and Information Sciences. Springer- Verlag. Berlin.
[Moreno, 2006]
J.A. Moreno.
A separation property of dissipative observers for nonlinear systems.
Proceedings of the 45th IEEE Conference on Decision and Control (CDC2006), pp. 1647-1652
[Teel et al., 2006]
Teel, A. R., R. G. Sanfelice, R. l. Goebel and Ch. Cai (2006). Workshop on robust hybrid systems: Theory and applications. In: Proceedings of 45th Conference on Decision and Control. IEEE. San Diego, Dec. 12-15.
[Thau, 1973]
F.E. Thau.
Observing the state of nonlinear dynamic systems.
Int J. Control, 17 (1973), pp. 471-479
[Van der Schaft, 2000]
A. Van der Schaft.
L2-Gain and Passivity Techniques in Nonlinear Control.
2nd, Springer-Verlag, (2000),
[Vargas and Moreno, 2005]
A. Vargas, J. Moreno.
Approximate high gain observers for non-lipschitz observability form.
International Journal of Control, 78 (2005), pp. 247-253
[Willems, 1972a]
J.C. Willems.
Dissipative dynamical systems, part I: General theory.
Archive for Rational Mechanics and Analysis, 45 (1972), pp. 321-351
[Willems, 1972b]
J.C. Willems.
Dissipative dynamical systems, part II: Linear systems with quadratic supply rates.
Archive for Rational Mechanics and Analysis, 45 (1972), pp. 352-393
[Xiong and Saif, 2001]
Y. Xiong, M. Saif.
Sliding mode observer for nonlinear uncertain systems.
IEEE Transactions on Automatic Control, 46 (2001), pp. 2012-2017
[Yakubovich et al., 2004]
V.A. Yakubovich, G.A. Leonov, A.Kh. Gelig.
Vibration and Control of Systems. World Scientific, (2004),
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