Online Exact Differentiation and Notion of Asymptotic Algebraic Observers

IEEE Transactions on Automatic Control

Volumn 48, Issue 11, 2003, Pages 2055-2060

  Ibrir, Salim ^a  

^a ÉCOLE DE TECHNOLOGIE SUPÉRIEURE   (Canada)

Author keywords

Exact differentiation; Nonlinear observers; System theory; Time varying systems

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTATIONAL METHODS; CONTROL SYSTEM ANALYSIS; DIFFERENTIATION (CALCULUS); MATHEMATICAL TRANSFORMATIONS; OBSERVABILITY; TIME VARYING CONTROL SYSTEMS;

INPUT-TO-STATE STABILITY (ISS); NONLINEAR OBSERVERS;

NONLINEAR CONTROL SYSTEMS;

EID: 0345690108     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.819303     Document Type: Article

References (37)

1. R. E. Kalman, "A new approach to linear filtering and prediction problems," Trans. ASME J. Basic Eng., vol. 82, no. D, pp. 35-45, 1960.
2. D. J. Luenberger, "An introduction to observers," IEEE Trans. Automat. Contr., vol. AC-16, pp. 596-602, Dec. 1971.
3. F. E. Thau, "Observing the state of nonlinear dynamic systems, " Int. J. Control, vol. 17, pp. 471-479, 1973.
4. S. Ibrir, "Algebraic riccati equation based differentiation trackers," AIAA J. Guid. Control Dyna., vol. 26, no. 3, pp. 502-505, 2003.
5. R. Rajamani, "Observers for lipschitz nonlinear systems," IEEE Trans. Automat. Contr., vol. 43, pp. 397-400, Mar. 1998.
6. S. Raghavan and J. K. Hedrick, "Observer design for a class of nonlinear systems," Int. J. Control, vol. 59, no. 2, pp. 515-528, 1994.
7. J. Doyle and G. Stein, "Robustness with observers," IEEE Trans. Automat. Contr., vol. AC-24, pp. 607-611, Aug. 1979.
8. M. Arcak and P. Kokotović, "Observer-based control of systems with slope-restricted nonlinearities," IEEE Trans. Automat Contr., vol. 46, pp. 1146-1150, July 2001.
9. J. P. Gauthier, H. Hammouri, and S. Othman, "A simple observer for nonlinear systems: Application to bioreactors," IEEE Trans. Automat. Contr., vol. 37, pp. 875-880, June 1992.
10. G. Ciccarella, M. D. Mora, and A. Germani, "A luenberger-like observer for nonlinear systems," Int. J. Control, vol. 57, no. 3, pp. 537-556, 1993.
11. A. Tomambè, "Asymptotic observers for nonlinear systems," Int. J. Syst. Sci., vol. 23, no. 3, pp. 435-442, 1992.
12. J. Tsinias, "Observer design for nonlinear systems," Syst. Control Lett., vol. 13, no. 2, pp. 135-142, 1989.
13. W. Kang and A. J. Krener, "Nonlinear observer design, a backstepping approach," presented at the AFOSR Workshop Dynamic Systems Control, Pasadena, CA, 1998.
14. M. Zeitz, "The extended luenberger observer for nonlinear systems," Syst. Control Lett., vol. 9, no. 2, pp. 149-156, 1987.
15. A. J. Krener and W. Respondek, "Nonlinear observers with linearizable error dynamics," SIAM J. Control Optim., vol. 23, no. 2, 1985.
16. H. Keller, "Nonlinear observer design by transformation into generalized observer canonical form," Int. J. Control, vol. 46, no. 6, pp. 1915-1930, 1987.
17. A. Glumineau, C. H. Moog, and F. Plestan, "New algebro-geometric conditions for the linearization by input-output injection," IEEE Trans. Automat. Contr., vol. 41, pp. 598-603, Apr. 1996.
18. A. G. V. Lopez-Morales and F. Plestan, "Linearization by completely generalized input output injection," Kybemetika, vol. 35, no. 6, pp. 793-802, 1999.
19. T. P. Proychev and R. L. Mishkov, "Transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input," Automatica, vol. 29, no. 2, pp. 495-498, 1993.
20. S. Diop, J. W. Grizzle, P. E. Morral, and A. G. Stefanoupoulou, "Interpolation and numerical differentiation for observer design," in Proc. Amer. Control Conf., Evanston, IL, 1993, pp. 1329-1333.
21. S. Ibrir and S. Diop, "Two numerical differentiation techniques for nonlinear state estimation," presented at the Amer. Control Conf., San Diego, CA, June 1999.
22. S. Ibrir, "Méthodes numériques pour la commande et l'observation des systèmes non linéaires," Ph.D. dissertation, Laboratoire des Signaux et Systèmes, Univ. Paris-Sud, Paris, France, 2000.
23. _, "New differentiators for control and observation applications," in Proc. Amer. Control Conf., 2001, pp. 2522-2527.
24. F. Esfandiari and K. H. Khalil, "Output feedback stabilization of fully linearizable systems," Int. J. Control, vol. 56, pp. 1007-1037, 1992.
25. A. M. Dabroom and H. K. Khalil, "Discrete-time implementation of high-gain observers for numerical differentiation," Int. J. Control, vol. 72, no. 17, pp. 1523-1537, 1999.
26. A. Levant, "Higher order sliding mode and arbitrary-order exact robust differentiation," in Proc. Euro. Control Conf., Sept, 2001, pp. 996-1001.
27. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. Washington, DC: National Bureau of Standards, 1964.
28. J. F. Ritt, Differential Algebra. Providence, RI: Amer. Math. Soc., 1950.
29. E. R. Kolchin, Differential Algebra and Algebraic Groups. New York: Academic, 1973.
30. L. A. Rubel and M. F. Singer, "A differentially algebraic elimination theorem with application to analog computability in the calculus of variations," in Proc. Amer. Math. Soc., vol. 94, 1985, pp. 653-658.
31. A. J. V. der Schaft, "On realization of nonlinear systems described by higher-order differential equations," Math. Syst. Theory, vol. 19, pp. 239-275, 1987.
32. L. Ljung and T. Gald, "On global identifiability for arbitrary model parametrizations," Automatica, vol. 30, no. 2, pp. 265-276, 1994.
33. A. R. Teel and L. Praly, "Tools for semi-global stabilization by partial state and output feedback," SIAM J. Control Optim., vol. 33, no. 5, pp. 1443-1488, Sept. 1995.
34. J. P. Gauthier and G. Bornard, "Observability for any u(t) of a class of nonlinear systems," IEEE Trans: Automat. Contr., vol. AC-26, pp. 922-926, 1981.
35. H. K. Khalil, Nonlinear Systems. New-York: Macmillan, 1991.
36. N. Kazantzis and C. Kravaris, "Nonlinear observer design for process monitoring," Ind. Eng. Chem. Res., vol. 39, pp. 408-419, 2000.
37. E. D. Sontag and Y. Wang, "On characterizations of the input-to-state stability property," Syst. Control Lett., vol. 24, pp. 351-359, 1995.