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Stable indirect fuzzy adaptive control. (English) Zbl 1037.93053
This paper proposes a stable indirect fuzzy adaptive control for MIMO (multi-input multi-output) continuous-time nonlinear systems. A TS (Takagi-Sugeno) fuzzy model-based observer is developed to approximate the nonlinear plant dynamic and estimate its state variables. This adaptive scheme presents the advantages that qualitative and analytic information about the plant operating can be used to design the fuzzy model rules and few rules (i.e. parameters) are to be tuned, which allows fast control update. This is a limiting factor for some applications. The proposed adaptive scheme achieves asymptotic tracking of a stable reference model, and the tracking and observation errors are shown to converge asymptotically to zero. The performance of this approach is evaluated on a two-link robot model.

93C42Fuzzy control systems
93C40Adaptive control systems
93C10Nonlinear control systems
Full Text: DOI
[1] Bestle, D.; Zietz, M.: Canonical form observer design for nonlinear time-variable systems. Internat. J. Control 38, 419-431 (1983) · Zbl 0521.93012
[2] Buckley, J. J.: Sugeno type controllers are universal controllers. Fuzzy sets and systems 53, 299-303 (1993) · Zbl 0785.93057
[3] Chen, C. S.; Chen, W. L.: Robust model reference adaptive control of nonlinear systems using fuzzy systems. Internat. J. Systems sci. 27, 1435-1442 (1996) · Zbl 0869.93026
[4] Chen, Y. C.; Teng, C. C.: A model reference control structure using a fuzzy neural networks. Fuzzy sets and systems 73, 291-312 (1995) · Zbl 0852.93053
[5] C. Fantuzzi, R. Rovatti, On the approximation capabilities of the homogeneous Takagi--Sugeno model, in: Proc. 5th IEEE Internat Conf. Fuzzy Syst., New Orleans, LA, September 1996, pp. 1067--1072.
[6] Krener, A. J.; Isidori, A.: Linearization by output injection and nonlinear observers. Systems and control lett. 3, 47-52 (1983) · Zbl 0524.93030
[7] Lin, W. -S.; Tsai, C. -H.: Neurofuzzy model-following control of MIMO nonlinear systems. IEE proc.-control theory appl. 146, 157-164 (1999)
[8] Ordonez, R.; Passino, K. M.: Stable multi-input multi-output adaptive fuzzy/neural control. IEEE trans. Fuzzy systems 7, No. 3, 345-353 (1999)
[9] Passino, K. M.; Yurkovich, S.: Fuzzy control. (1998) · Zbl 0925.93530
[10] R. Rovatti, Takagi--Sugeno models as approximators in Sobolev norms, in: Proc. 5th IEEE Internat. Conf. Fuzzy Systems, New Orleans, LA, September 1996, pp. 1060--1066.
[11] Sastry, S.; Bosdon, M.: Adaptive control: stability, convergence and robustness. (1989)
[12] Su, C. Y.; Stepanenko, Y.: Adaptive control of a class of nonlinear systems with fuzzy logic. IEEE trans. Fuzzy systems 2, 285-294 (1994)
[13] Takagi, T.; Seguno, M.: Fuzzy identification of systems and its application to modeling and control. IEEE trans. Systems man cybernet. 15, 116-132 (1985) · Zbl 0576.93021
[14] Tong, S.: Fuzzy adaptive control of multivariable nonlinear systems. Fuzzy sets and systems 111, 169-182 (2000) · Zbl 0976.93050
[15] Tong, S.; Wang, T.; Tang, J. T.: Fuzzy adaptive output tracking control of nonlinear systems. Fuzzy sets and systems 111, 153-167 (2000) · Zbl 0976.93049
[16] Vidyasagar, M.: Nonlinear systems analysis. (1993) · Zbl 0900.93132
[17] Wang, L. X.: Adaptive fuzzy systems and control: design and stability analysis. (1994)
[18] Ying, H.: Sufficient conditions on general fuzzy systems as function approximators. Automatica 30, 521-525 (1994) · Zbl 0800.93708