Extensions of sliding-mode adaptive observer are presented for state reconstruction of nonlinear systems with uncertainty having unknown bounds. The observer uses nonlinear gains that are smoothened versions of classical sliding-mode gains and they are continuously updated to guarantee a globally stable observation error. This observer is applied to Chua’s circuit in a chaotic synchronization scheme. A generalization to known waveform type disturbances and measurement uncertainties is pointed out. [S0022-0434(00)02304-2]
1.
Walcott
, B. L.
, and Zak
, S. H.
, 1987
, “State observation of nonlinear uncertain dynamical systems
,” IEEE Trans. Autom. Control
, 32
, pp. 166
–170
.2.
Walcott
, B. L.
, Corless
, M. J.
, and Zak
, S. H.
, 1987
, “Comparative study of non-linear state-observation technique
,” Int. J. Control
, 45
, pp. 2109
–2132
.3.
Slotine
, J-J. E.
, Hedrick
, J. K.
, and Misawa
, E. A.
, 1986
, “On sliding observers
,” ASME J. Dyn. Syst., Meas., Control
, 109
, pp. 245
–252
.4.
Ruelle, D., 1989, Elements of Differentiable Dynamics and Bifurcation Theory, Academic Press, San Diego.
5.
Bestle
, D.
, and Zeitz
, M.
, 1983
, “Canonical form observer design for nonlinear time-variable systems
,” Int. J. Control
, 38
, pp. 419
–431
.6.
Krener
, A. J.
, and Respondek
, W.
, 1985
, “Nonlinear observer with linearizable error dynamics
,” SIAM J. Control Optim.
, 23
, pp. 197
–216
.7.
Isidori, A., 1985, Nonlinear Control Systems: An Introduction, Springer-Verlag, Berlin.
8.
Baumann
, W.
, and Rugh
, W.
, 1986
, “Feedback control of non-linear systems by extended linearization
,” IEEE Trans. Autom. Control
, 31
, pp. 40
–47
.9.
Thau
, F. E.
, 1973
, “Observing the state of non-linear dynamic systems
,” Int. J. Control
, 18
, pp. 471
–479
.10.
Kou
, S. R.
, Elliot
, D. L.
, and Tarn
, T. J.
, 1975
, “Exponential observer for nonlinear dynamic systems
,” Inf. Control.
, 29
, pp. 204
–216
.11.
Vidyasagar
, M.
, 1980
, “On the stabilization of nonlinear systems using state detection
,” IEEE Trans. Autom. Control
, 25
, pp. 504
–509
.12.
Yaz
, E.
, and Azemi
, A.
, 1993
, “Observer design for discrete and continuous nonlinear stochastic systems
,” Int. J. Syst. Sci.
, 21
, pp. 2289
–2302
.13.
Yaz
, E.
, and Azemi
, A.
, 1993
, “Sliding mode observers for nonlinear models with unbounded noise and measurement uncertainties
,” Dynamics & Control
, 3
, pp. 217
–235
.14.
Corless
, M.
, and Leitmann
, G.
, 1983
, “Adaptive control of systems containing uncertain functions and unknown functions with uncertain bounds
,” JOTA
, 41
, pp. 155
–168
.15.
Chen
, Y. H.
, 1989
, “Modified adaptive robust control system design
,” Int. J. Control
, 49
, pp. 1869
–1882
.16.
Chen
, Y. H.
, 1989
, “State estimation for non-linear uncertain systems: a design based on properties related to the uncertainty bound
,” Int. J. Control
, 52
, pp. 1131
–1146
.17.
Chen
, Y. H.
, 1992
, “Adaptive robust control of uncertain systems with measurement noise
,” Automatica
, 28
, pp. 715
–728
.18.
Yoo
, D. S.
, and Chung
, M. J.
, 1992
, “A variable structure control with simple adaptation laws for upper bounds on the norm of the uncertainties
,” IEEE Trans. Autom. Control
, 37
, pp. 860
–865
.19.
Carroll
, T. L.
, and Pecora
, L. M.
, 1991
, “Synchronizing chaotic circuits
,” IEEE Trans. Circuits Syst.
, 38
, pp. 453
–456
.20.
Ogorzalek
, M. J.
, 1993
, “Taming Chaos-Part I: Synchronization
,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
, 40
, pp. 693
–699
.21.
Nijmeijer
, H.
, and Mareels
, I. M. Y.
, 1997
, “An observer looks at synchronization
,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
, 44
, pp. 882
–890
.22.
Sobiski
, D. J.
, and Thorp
, J. S.
, 1998
, “PDMA-1: Chaotic Communication via the EKF
,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
, 45
, pp. 194
–197
.23.
Chua
, L.
, Wu
, C.
, Hung
, A.
, and Zhong
, G.
, 1993
, “A universal circuit for studying and generating chaos-part I: routes to chaos
,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
, 40
, pp. 732
–744
.24.
Slotine, J-J. E., and Li, W., 1991, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, NJ.
25.
Johnson
, C. D.
, 1980
, “Disturbance accommodation control: an overview of the subject
,” J. Interdis. Model and Simul.
, 3
, pp. 1
–29
.26.
Yaz
, E.
, and Azemi
, A.
, 1993
, “Variable structure observer with a boundary-layer for correlated noise/disturbance models and disturbance minimization
,” Int. J. Control
, 57
, pp. 1191
–1206
.27.
Azemi
, A.
, and Yaz
, E.
, 1993
, “Dynamic disturbance minimization control for discrete nonlinear stochastic systems
,” Optimal Control Applications & Methods
, 14
, pp. 181
–194
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