Adaptive Fuzzy Control for a Class of Nonlinear Systems with State Observer
Faculty of Management Information Sciences, Prefectural University of Hiroshima, 1-1-71 Ujina-higashi, Minami-ku, Hiroshima 734-8558, Japan
This paper addresses the fuzzy control problem using the Lyapunov synthesis approach. In order to deal with cases where the system state is unavailable, a state observer is proposed. Consequently, the whole system behavior can be attributed to a kind of standard singularly perturbed form. At the same time, to deal with the gap, if any, between the real state and its estimated value from the state observer, we view it as a part of system disturbance, and propose a unique way to deal with the disturbance, i.e., adopt a switching function with an alterable coefficient, which is tuned by adaptive law based on the tracking error between the output of the considered system and the desired value. Finally, it is shown that the fuzzy controller proposed guarantees the tracking error will shrink to zero, while maintaining the stability of all signals involved in the system.
-  C. C. Lee, “Fuzzy logic in control systems: Fuzzy logic controller, part I and part II,” IEEE Trans. on Systems, Man, and Cybernetics, Vol.20, pp. 404-435, 1990.
-  L.-X. Wang, and J. M. Mendel, “Fuzzy basis functions, universal approximation, and orthogonal least-squares learning,” IEEE Trans. on Neural Networks, Vol.3, pp. 807-813, 1992.
-  L.-X. Wang, “Stable adaptive fuzzy control of nonlinear systems,” IEEE trans. Fuzzy Systems, Vol.1, No.2, pp. 146-155, 1993.
-  N. Golea, A. Glolea, and K. Benmahammed, “Fuzzy model reference adaptive control,” IEEE Trans. on Fuzzy Systems, Vol.10, No.4, pp. 436-444, 2002.
-  S. Tong, and H.-X. Li, “Fuzzy adaptive sliding-mode control for MIMO nonlinear systems,” IEEE Trans. on Fuzzy Systems, Vol.11, No.3, pp. 354-360, 2003.
-  X.-J. Ma, Z.-Q. Sun, and Y.-Y. He, “Analysis and design of fuzzy controller and fuzzy observer,” IEEE Trans. on Fuzzy Systems, Vol.6, No.1, pp. 41-51, 1998.
-  Y. G. Leu, and W. Y. Wang, “Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems,” IEEE Trans. on Systems, Man, and Cybernetics, Vol.29, pp. 583-591, 1999.
-  C.-H. Wang, H.-L. Liu, and T.-C. Lin, “Direct adaptive fuzzyneural control with state observer and supervisory controller for unknown nonlinear dynamical systems,” IEEE Trans. on Fuzzy Systems, Vol.10, No.1, pp. 39-49, 2002.
-  P. Ascencio, D. Sbarbaro, and H. B. Verbruggen, “An adaptive fyzzy hybrid state observer for bioprocesses,” IEEE Trans. on Fuzzy Systems, Vol.12, No.5, pp. 641-651, 2004.
-  F. Esfandiari, and H. K. Khalil, “Output feedback stabilization of fully linearizable systems,” Int. J. Control, Vol.56, No.5, pp. 1007-1037, 1992.
-  H. K. Khalil, “Robust servomechanism output feedback controllers for feedback linearizable sytems,” Automatica, Vol.30, No.10, pp. 1587-1599, 1994.
-  H. K. Khalil, “Adaptive output feedback control of nonlinear systems represented by input-output models,” IEEE Trans. on Automatic Control, Vol.41, No.2, pp. 177-188, 1996.
-  C.-Y. Su, and Y. Stepanenko, “Adaptive control of a class of nonlinear systems with fuzzy logic,” IEEE trans. Fuzzy Systems, Vol.2, No.4, pp. 285-294, 1994.
-  M. M. Polycarpou, “Stable adaptive neural control scheme for nonlinear systems,” IEEE Trans. on Automatic Control, Vol.41, No.3, pp. 447-451, 1996.
-  M. M. Polycarpou, and M. J. Mears, “Stable adaptive tracking of uncertain systems using nonlinear parameterized on-line approximators,” Int. J. Control, Vol.73, No.3, pp. 363-384, 1998.
-  H. Han, C.-Y. Su, and Y. Stepanenko, “Adaptive control of a class of nonlinear systems with nonlinearly parameterized fuzzy approximators,” IEEE Trans. on Fuzzy Systems, Vol.9, No.2, pp. 315-323, 2001.
-  C.-L. Hwang, “A novel Takagi-Sugeno-based robust adaptive fuzzy sliding-mode control,” IEEE Trans. on Fuzzy Systems, Vol.12, No.5, pp. 676-687, 2004.
-  J.-J. Slotine, and J. A. Coetsee, “Adaptive sliding controller synthesis for nonlinear systems,” Int. J. Control, Vol.43, pp. 1631-1651, 1986.
-  P. Rainer, “Robust control by fuzzy sliding mode,” Automatica, Vol.30, No.9, pp. 1429-1437, 1994.
-  P. V. Kokotovic, H. K. Khalil, and J. O’Reilly, “Singular Perturbation Methods in Control: Analysis and Design,” Academic Press, 1986.
-  G.-C. Hwang, and S.-C. Lin, “A stability approach to fuzzy control design for nonlinear systems,” Fuzzy Sets and Systems, No.8, pp. 279-287, 1992.
-  E. Kim, “A fuzzy disturbance observer and its application to control,” IEEE Trans. on Fuzzy Systems, Vol.10, No.1, pp. 77-84, 2002.
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