Closed-Loop Behavior of a Class of Nonlinear Systems under EKF-Based Control

IEEE Transactions on Automatic Control

Volumn 52, Issue 3, 2007, Pages 536-540

  Ahrens, Jeffrey H ^a   Khalil, Hassan K ^a  

^a Michigan State University   (United States)

Author keywords

Kalman filtering; nonlinear control; observers; output feedback control; singular perturbation

Indexed keywords

EID: 85008047685     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/TAC.2007.892376     Document Type: Article

References (20)

1. J. H. Ahrens, “Design and performance tradeoffs of high-gain observers with applications to smart material actuated systems,” Ph.D. dissertation, Michigan State Univ., East Lansing, MI, 2006.
2. A. N. Atassi and H. K. Khalil, “A separation principle for the stabilization of a class of nonlinear systems,” IEEE Trans. Autom. Control, vol. 44, no. 9, pp. 1672–1687, Sep. 1999.
3. J. S. Baras, A. Bensoussan, and M. R. James, “Dynamic observers as asymptotic limits of recursive filters: Special cases,” SIAM J. Appl. Math., vol. 48, no. 5, pp. 1147–1158, 1988.
4. M. Boutayeb and D. Aubry, “A strong tracking extended Kalman observer for nonlinear discrete-time systems,” IEEE Trans. Autom. Control, vol. 44, no. 8, pp. 1550–1556, Aug. 1999.
5. M. Boutayeb, H. Rafaralahy, and M. Darouach, “Convergence analysis of the extended Kalman filter used as an observer for nonlinear deterministic discrete-time systems,” IEEE Trans. Autom. Control, vol. 42, no. 4, pp. 581–586, Apr. 1997.
6. F. M. Callier, J. Winkin, and J. L. Willems, “Convergence of the time-invariant Riccati differential equation and LQ-problem: Mechanisms of attraction,” Int. J. Control, vol. 59, pp. 983–1000, 1994.
7. Y. Chitour, “Time-varying high-gain observers for numerical differentiation,” IEEE Trans. Autom. Control, vol. 47, no. 9, pp. 1565–1569, Sep. 2002.
8. F. Deza, E. Busvelle, J. P. Gauthier, and D. Rakotopara, “High gain estimation for nonlinear systems,” Syst. Control Lett., vol. 18, pp. 295–299, 1992.
9. A. Gelb, Applied Optimal Estimation. Cambridge, MA: MIT Press, 1974.
10. S. Ibrir, “Linear time-derivative trackers,” Automatica, vol. 40, pp. 397-405, 2004.
11. A. Isidori, Nonlinear Control Systems II. New York: Springer-Verlag, 1999.
12. H. K. Khalil, Nonlinear Systems, 3rd ed. Upper Saddle River, NJ: Prentice-Hall, 2002.
13. H. K. Khalil, “Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems,” IEEE Trans. Autom. Control., vol. 49, no. 12, pp. 2173–2184, Dec. 2004.
14. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems. New York: Wiley-Interscience, 1972.
15. K. Reif, F. Sonnemann, and R. Unbehauen, “An EKF-based nonlinear observer with a prescribed degree of stability,” Automatica, vol. 34, pp. 1119–1123, 1998.
16. K. Reif and R. Unbehauen, “The extended Kalman filter as an exponential observer for nonlinear systems,” IEEE Trans. Signal Process., vol. 47, no. 8, pp. 2324–2328, Aug. 1999.
17. Y. K. Song and J. W. Grizzle, “The extended Kalman filter as a local asymptotic observer for nonlinear discrete-time systems,” J. Math. Syst., Estimat. Control, vol. 5, pp. 59–78, 1995.
18. H. Sorenson, “Guest editorial: On applications of Kalman filtering,” IEEE Trans. Autom. Control, vol. AC-28, no. 3, pp. 254–255, Mar. 1983.
19. A. R. Teel and J. Hespanha, “Examples of GES systems that can be driven to infinity by arbitrarily small additive decaying exponentials,” IEEE Trans. Autom. Control, vol. 49, no. 8, pp. 1407–1410, Aug. 2004.
20. F. Viel, E. Busvelle, and J. P. Gauthier, “Stability of polymerization reactors using I/O linearization and a high-gain observer,” Automatica, vol. 31, pp. 971–984, 1995.