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TECHNICAL PAPERS

Nonlinear State Estimation by Adaptive Embedded RBF Modules

[+] Author and Article Information
Chengyu Gan, Kourosh Danai

Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003-2210

J. Dyn. Sys., Meas., Control 123(1), 44-48 (Oct 05, 1999) (5 pages) doi:10.1115/1.1341198 History: Received October 05, 1999
Copyright © 2001 by ASME
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References

Krstic, M., Kanellakopoulos, I., and Kokotovic, P., 1995, Nonlinear and Adaptive Control Design, Wiley, New York, NY.
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.
Gelb, A., 1974, Applied Optimal Estimation, MIT Press, Cambridge, MA.
Luenberger,  D. G., 1971, “An introduction to observers,” IEEE Trans. Autom. Control, AC16, No. 6, pp. 596–602.
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.
Bestle,  D., and Zeitz,  M., 1993, “Canonical form observer design for nonlinear time-variable systems,” Int. J. Control, 38, No. 2, pp. 419–431.
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.
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.
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.
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.
Vidyasagar, M., 1993, Nonlinear Systems Analysis, Prentice-Hall, Englewood Cliffs, NJ.
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.
Sorenson, H. W., 1985, Kalman Filtering: Theory and Application, IEEE Press, New York, N.Y.
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.
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.
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.
Drakunov,  S. V., 1983, “An adaptive quasioptimal filter with discontinuous parameters,” Autom. Remote Control, 44, No. 2, pp. 76–86.
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.
Krener,  A. J., and Isidori,  W., 1983, “Linearization by output injection and nonlinear observer,” Syst. Control Lett., 3, pp. 47–52.
Narendra, K. S., and Annaswamy, A. M., 1989, Stable Adaptive Systems Prentice Hall, Englewood Cliffs, NJ.
Kreisselmeier,  G., 1977, “Adaptive observers with exponential rate of convergence,” IEEE Trans. Autom. Control, 22, pp. 2–8.
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.
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.
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.
Ljung,  L., 1977, “Analysis of recurive stochastic algorithms,” IEEE Trans. Autom. Control, AC22, No. 4, pp. 551–575.
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.

Figures

Grahic Jump Location
Illustration of the modified sub-function when embedded by an RBF network
Grahic Jump Location
Estimated values (dotted line) of the load torque τL by EKF using the nominal model
Grahic Jump Location
Estimated values of the load torque by EKF using the RBF-embedded model
Grahic Jump Location
Estimated values of the states Rotor Flux1 and Rotor Flux2 by EKF using the RBF-embedded model
Grahic Jump Location
The relationship between the modified sub-function τL and τL as obtained by adapting the RBF weights

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