Nonlinear observers for locally uniformly observable systems

Hassan Hammouri; M. Farza

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 9, page 353-370
  • ISSN: 1292-8119

Abstract

top
This paper deals with the observability analysis and the observer synthesis of a class of nonlinear systems. In the single output case, it is known [4-6] that systems which are observable independently of the inputs, admit an observable canonical form. These systems are called uniformly observable systems. Moreover, a high gain observer for these systems can be designed on the basis of this canonical form. In this paper, we extend the above results to multi-output uniformly observable systems. Corresponding canonical forms are presented and sufficient conditions which permit the design of constant and high gain observers for these systems are given.

How to cite

top

Hammouri, Hassan, and Farza, M.. "Nonlinear observers for locally uniformly observable systems." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 353-370. <http://eudml.org/doc/90700>.

@article{Hammouri2010,
abstract = { This paper deals with the observability analysis and the observer synthesis of a class of nonlinear systems. In the single output case, it is known [4-6] that systems which are observable independently of the inputs, admit an observable canonical form. These systems are called uniformly observable systems. Moreover, a high gain observer for these systems can be designed on the basis of this canonical form. In this paper, we extend the above results to multi-output uniformly observable systems. Corresponding canonical forms are presented and sufficient conditions which permit the design of constant and high gain observers for these systems are given. },
author = {Hammouri, Hassan, Farza, M.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Nonlinear systems; uniform observability; nonlinear observer.; nonlinear systems; nonlinear observer},
language = {eng},
month = {3},
pages = {353-370},
publisher = {EDP Sciences},
title = {Nonlinear observers for locally uniformly observable systems},
url = {http://eudml.org/doc/90700},
volume = {9},
year = {2010},
}

TY - JOUR
AU - Hammouri, Hassan
AU - Farza, M.
TI - Nonlinear observers for locally uniformly observable systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 9
SP - 353
EP - 370
AB - This paper deals with the observability analysis and the observer synthesis of a class of nonlinear systems. In the single output case, it is known [4-6] that systems which are observable independently of the inputs, admit an observable canonical form. These systems are called uniformly observable systems. Moreover, a high gain observer for these systems can be designed on the basis of this canonical form. In this paper, we extend the above results to multi-output uniformly observable systems. Corresponding canonical forms are presented and sufficient conditions which permit the design of constant and high gain observers for these systems are given.
LA - eng
KW - Nonlinear systems; uniform observability; nonlinear observer.; nonlinear systems; nonlinear observer
UR - http://eudml.org/doc/90700
ER -

References

top
  1. G. Besançon and H. Hammouri, On uniform observation of non uniformly observable systems. Systems Control Lett.29 (1996) 9-19.  
  2. G. Besançon and H. Hammouri, On observer design for interconnected systems. J. Math. Systems Estim. Control 8 (1998).  
  3. G. Bornard and H. Hammouri, A high gain observer for a class of uniformly observable systems, in Proc. 30th IEEE Conference on Decision and Control Brighton 122 (1991) 176-192.  
  4. J.P. Gauthier and G. Bornard, Observability for any u(t) of a class of nonlinear systems. IEEE Trans. Automat. Control26 (1981) 922-926.  
  5. J.P. Gauthier, H. Hammouri and S. Othman, A simple observer for nonlinear systems - Application to bioreactors. IEEE Trans. Automat. Control37 (1992) 875-880.  
  6. J.P. Gauthier and I.A.K. Kupka, Observability and observers for nonlinear systems. SIAM J. Control Optim.32 (1994) 975-994.  
  7. J.P. Gauthier and I.A.K. Kupka, Observability for systems with more outputs than inputs. Math. Z.223 (1996) 47-78.  
  8. J.P. Gauthier and I.A.K. Kupka, Deterministic Observation Theory and Applications. Cambridge University Press (2001).  
  9. R. Hermann and A.J. Krener, Nonlinear controllability and observability. IEEE Trans. Automat. Control22 (1977) 728-740.  
  10. A. Isidori, Nonlinear control systems: An introducion, Vol. 72. Springer, Berlin (1985).  
  11. A.J. Krener and A. Isidori, Linearization by output injection and nonlinear observers. System Control Lett.3 (1983) 47-52.  
  12. A.J. Krener and W. Respondek, Nonlinear observers with linealizable error dynamics. SIAM J. Control Optim.23 (1985) 197-216.  
  13. H.J. Sussman, Single-input observability of continuous-time systems. Math. System Theory12 (1979) 371-393.  
  14. F.E. Thau, Observing the state of nonlinear dynamics systems. Int. J. Control17 (1973) 471-479.  
  15. D. Williamson, Observability of bilinear systems, with application to biological control. Automatica32 (1977) 143-254.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.