A modeling compensation method is introduced to enhance the performance of the extended Kalman filter (EKF) in coping with the uncertainty of estimation model. In this method, single-input single-output radial basis function (RBF) modules are embedded within the nonlinear estimation model to provide additional degrees of freedom for model adaptation. The weights of the embedded RBF modules are adapted by the EKF, concurrent with state estimation. This compensation method is tested in application to a benchmark problem. Simulation results indicate that the RBF modules provide the means to model the uncertain components of the estimation model within their range of variation.
Issue Section:
Technical Papers
1.
Krstic, M., Kanellakopoulos, I., and Kokotovic, P., 1995, Nonlinear and Adaptive Control Design, Wiley, New York, NY.
2.
Frank
, P. M.
, 1990
, “Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy-a survey and some new results
,” Automatica
, 26
, No. 2
, pp. 459
–474
.3.
Gelb, A., 1974, Applied Optimal Estimation, MIT Press, Cambridge, MA.
4.
Luenberger
, D. G.
, 1971
, “An introduction to observers
,” IEEE Trans. Autom. Control
, AC16
, No. 6
, pp. 596
–602
.5.
Tse
, E.
, and Athans
, M.
, 1970
, “Optimal minimal-order observer estimators for discrete linear time-varying systems
,” IEEE Trans. Autom. Control
, AC-15
, pp. 416
–426
.6.
Bestle
, D.
, and Zeitz
, M.
, 1993
, “Canonical form observer design for nonlinear time-variable systems
,” Int. J. Control
, 38
, No. 2
, pp. 419
–431
.7.
Gauthier
, J. P.
, and Kupka
, I. A. K.
, 1994
, “Observability and observer for nonlinear systems
,” SIAM J. Control Optim.
, 32
, No. 4
, pp. 975
–994
.8.
Chao
, C. T.
, and Teng
, C. C.
, 1996
, “A fuzzy neural network based extended kalman filter
,” Int. J. Syst. Sci.
, 27
, No. 3
, pp. 333
–339
.9.
Kim
, Y. H.
, Frank
, L. L.
, and Chaouki
, T. A.
, 1997
, “A dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems
,” Automatica
, 33
, No. 8
, pp. 1539
–1543
.10.
Gauthier
, J. P.
, Hammouri
, H.
, and Othman
, S.
, 1992
, “A simple observer for nonlinear systems: application to bioreactors
,” IEEE Trans. Autom. Control
, 37
, pp. 875
–880
.11.
Vidyasagar, M., 1993, Nonlinear Systems Analysis, Prentice-Hall, Englewood Cliffs, NJ.
12.
Misawa
, E. A.
, and Hedrick
, J. K.
, 1989
, “Nonlinear observer-a state of the art survey
,” ASME J. Dyn. Syst., Meas., Control
, 111
, pp. 344
–352
.13.
Sorenson, H. W., 1985, Kalman Filtering: Theory and Application, IEEE Press, New York, N.Y.
14.
Song, Y., and Grizzle, J. W., 1992, “The extended kalman filter as a local asymptotic observer for nonlinear discrete-time systems,” in Proc. of the American Control Conference, Chicago, IL, pp. 3365–3369.
15.
Drakunov, S., 1992, “Sliding mode observers based on equivalent control method,” Proc. of the 31st IEEE Conf. on Decision and Control, Tucson, Arizona, pp. 2368–2369.
16.
Krishnaswami, V., and Rizzoni, G., 1995, “Vehicle steering system state estimation using sliding mode observers,” Proc. of the 34th Conference on Decision & Control, New Orleans, LA, pp. 3391–3396.
17.
Drakunov
, S. V.
, 1983
, “An adaptive quasioptimal filter with discontinuous parameters
,” Autom. Remote Control
, 44
, No. 2
, pp. 76
–86
.18.
Slotine
, J. E.
, Hedrick
, J. K.
, and Hedrick
, M. E. A.
, 1987
, “On sliding observers
,” ASME J. Dyn. Syst., Meas., Control
, 109
, pp. 245
–252
.19.
Krener
, A. J.
, and Isidori
, W.
, 1983
, “Linearization by output injection and nonlinear observer
,” Syst. Control Lett.
, 3
, pp. 47
–52
.20.
Narendra, K. S., and Annaswamy, A. M., 1989, Stable Adaptive Systems Prentice Hall, Englewood Cliffs, NJ.
21.
Kreisselmeier
, G.
, 1977
, “Adaptive observers with exponential rate of convergence
,” IEEE Trans. Autom. Control
, 22
, pp. 2
–8
.22.
Shoureshi, R., and Chu, R., 1993, “Hopfield-based adaptive observers: next generation of luenberger state estimators,” IEEE Int. Conference on Neural Networks, Piscataway, New Jersey, Apr., pp. 1289–1294.
23.
Gan, C., 2000, “Embedded radial basis function networks to compensate for modeling uncertainty of nonlinear dynamic systems,” Doctoral dissertation, University of Massachusetts Amherst, Department of Mechanical and Industrial Engineering.
24.
Ljung
, L.
, 1979
, “Asymptotic behavior of the extended kalman filter as a parameter estimator for linear systems
,” IEEE Trans. Autom. Control
, AC24
, No. 1
, pp. 36
–50
.25.
Ljung
, L.
, 1977
, “Analysis of recurive stochastic algorithms
,” IEEE Trans. Autom. Control
, AC22
, No. 4
, pp. 551
–575
.26.
Ortega, R., Chang, G., and Mendes, E., 1998, Control of Induction Motors: A Benchmark Problem, for Nonlinear Control. http://www.supelec.fr/invi/lss/fr/personels/ortega/benchmi/benchmi.html.
Copyright © 2001
by ASME
You do not currently have access to this content.