×

zbMATH — the first resource for mathematics

Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction. (English) Zbl 1217.93086
Summary: This paper investigates fuzzy adaptive control schemes for a class of Multi-Input Multi-Output (MIMO) unknown nonlinear systems with known and unknown sign of the control gain matrix. Three fuzzy adaptive control schemes are developed. In the design of the second and third controller, we exploit a decomposition of the control gain matrix into a symmetric positive-definite matrix, a diagonal matrix with diagonal entries \(+1\) or \(-1\) and a unity upper triangular matrix. The Nussbaum-type function is used to deal with the unknown control direction (i.e., the unknown sign of the control gain matrix). For updating the parameters of the fuzzy system, an adaptation proportional-integral law is proposed. Theoretical results are illustrated through two simulation examples.

MSC:
93C42 Fuzzy control/observation systems
93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Boulkroune, A.; Tadjine, M.; Msaad, M.; Farza, M., A unified approach for design of indirect adaptive output-feedback fuzzy controller, Int. J. intell. systems technol. appl., 5, 1/2, 83-103, (2008)
[2] Boulkroune, A.; Tadjine, M.; Msaad, M.; Farza, M., How to design a fuzzy adaptive control based on observers for uncertain affine nonlinear systems, Fuzzy sets and systems, 159, 926-948, (2008) · Zbl 1170.93335
[3] Chang, Y.C., Robust tracking control for nonlinear MIMO systems via fuzzy approaches, Automatica, 36, 1535-1545, (2000) · Zbl 0967.93060
[4] Chang, Y.C., Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSS and \(H^\infty\) approaches, IEEE trans. fuzzy systems, 9, 278-292, (2001)
[5] Chekireb, H.; Tadjine, M.; Bouchaffra, D., Direct adaptive fuzzy control of nonlinear system class with applications, Control intell. systems, 31, 2, 1-11, (2003) · Zbl 1082.93539
[6] J. Chen, A. Behal, D.M. Dawson, Adaptive output feedback control for a class of MIMO nonlinear systems, in: Proc. American Control Conf., Minneapolis, MN, 2006, pp. 5300-5305.
[7] Costa, R.R.; Hsu, L.; Imai, A.K.; Kokotovic, P., Lyapunov-based adaptive control of MIMO systems, Automatica, 39, 7, 1251-1257, (2003) · Zbl 1029.93041
[8] Essounbouli, N.; Hamzaoui, A.; Zaytoon, J., An improved robust adaptive fuzzy controller for MIMO systems, Control intell. systems, 34, 1, 12-21, (2006) · Zbl 1172.93360
[9] Ge, S.S.; Hang, C.C.; Lee, T.H.; Zhang, T., Stable adaptive neural network control, (2001), Kluwer Academic Publisher Boston · Zbl 1001.93002
[10] Ge, S.S.; Wang, J., Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems, IEEE trans. neural networks, 13, 6, 1409-1419, (2002)
[11] Golea, N.; Golea, A.; Benmahammed, K., Stable indirect fuzzy adaptive control, Fuzzy sets and systems, 137, 353-366, (2003) · Zbl 1037.93053
[12] Hsu, L.; Costa, R.R.; Lizarralde, F., Lyapunov/passivity-based adaptive control of relative degree two MIMO systems with an application to visual servoing, IEEE trans. automat. control, 52, 2, 364-371, (2007) · Zbl 1366.93291
[13] Labiod, S.; Boucherit, M.S.; Guerra, T.M., Adaptive fuzzy control of a class of MIMO nonlinear systems, Fuzzy sets and systems, 151, 59-77, (2005) · Zbl 1142.93365
[14] Labiod, S.; Guerra, T.M., Direct adaptive fuzzy control for a class of MIMO nonlinear systems, Int. J. systems sci., 38, 8, 665-675, (2007) · Zbl 1128.93032
[15] Lee, H.; Tomizuka, M., Robust adaptive control using a universal approximator for SISO nonlinear systems, IEEE trans. fuzzy systems, 8, 1, 95-106, (2000)
[16] Li, H.X.; Tong, S.C., A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems, IEEE trans. fuzzy systems, 11, 1, 24-34, (2003)
[17] Narendra, K.S.; Annaswamy, M.A., A new adaptive law for robust adaptive control without persistent excitation, IEEE trans. automat. control, 32, 134-145, (1987) · Zbl 0617.93035
[18] Nussbaum, R.D., Some remarks on the conjecture in parameter adaptive control, Systems control lett., 3, 5, 243-246, (1983) · Zbl 0524.93037
[19] Ordonez, R.; Passino, K.M., Stable multi-input multi-output adaptive fuzzy/neural control, IEEE trans. fuzzy systems, 7, 3, 345-353, (1999)
[20] Perlis, S., Theory of matrices, (1991), Dover Publications New York
[21] Sanner, R.M.; Slotine, J.E., Gaussian networks for direct adaptive control, IEEE trans. neural networks, 3, 6, 837-863, (1992)
[22] Slotine, J.E.; Li, W., Applied nonlinear control, (1991), Prentice-Hall Englewood Cliffs, NJ · Zbl 0753.93036
[23] Spooner, J.T.; Passino, K.M., Stable adaptive control using fuzzy systems and neural networks, IEEE trans. fuzzy systems, 4, 339-359, (1996)
[24] Strang, G., Linear algebra and its applications, (1980), Academic Press Inc. New York · Zbl 0463.15001
[25] Su, C.Y.; Stepanenko, Y., Adaptive control of a class of nonlinear systems with fuzzy logic, IEEE trans. fuzzy systems, 2, 285-294, (1994)
[26] Tang, Y.; Zhang, N.; Li, Y., Stable fuzzy adaptive control for a class of nonlinear systems, Fuzzy sets and systems, 104, 279-288, (1999) · Zbl 0942.93018
[27] Tong, S.C.; Li, Q.; Chai, T., Fuzzy adaptive control of a class of nonlinear systems, Fuzzy sets and systems, 101, 31-39, (1999) · Zbl 0952.93077
[28] Tong, S.C.; Tang, J.; Wang, T., Fuzzy adaptive control of multivariable nonlinear systems, Fuzzy sets and systems, 111, 2, 153-167, (2000) · Zbl 0976.93049
[29] Tong, S.C.; Li, H.X., Fuzzy adaptive sliding model control for MIMO nonlinear systems, IEEE trans. fuzzy systems, 11, 3, 354-360, (2003)
[30] Tong, S.C.; Chen, B.; Wang, Y., Fuzzy adaptive output feedback control for MIMO nonlinear systems, Fuzzy sets and systems, 156, 2, 285-299, (2005) · Zbl 1082.93032
[31] Wang, L.X., Adaptive fuzzy systems and control: design and stability analysis, (1994), Prentice-Hall Englewood Cliffs, NJ
[32] Ye, X.D., Adaptive nonlinear output-feedback control with unknown high-frequency gain sign, IEEE trans. automat. control, 46, 1, 112-115, (2001) · Zbl 1062.93517
[33] Zhang, T.P.; Ge, S.S., Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs, Automatica, 43, 6, 1021-1033, (2007) · Zbl 1282.93152
[34] Zhang, T.P.; Yi, Y., Adaptive fuzzy control for a class of MIMO nonlinear systems with unknown dead-zones, Acta automat. sinica, 33, 1, 96-99, (2007)
[35] X.T. Zhang, D.M. Dawson, M.S. De Queiroz, B. Xian, Adaptive control for a class of MIMO nonlinear systems with non-symmetric input matrix, in: Proc. IEEE International Conf. on Control Applications, Taipei, Taiwan, 2004, pp. 1324-1329.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.