×

zbMATH — the first resource for mathematics

Adaptive fuzzy controller for multivariable nonlinear state time-varying delay systems subject to input nonlinearities. (English) Zbl 1217.93085
Summary: An adaptive fuzzy variable-structure controller is investigated for a class of uncertain Multi-Input Multi-Output (MIMO) nonlinear time-delay systems with both sector nonlinearities and dead-zones. A decomposition property of the control-gain matrix is fully exploited in the controller design and the stability analysis. The unknown time-varying delay uncertainties are compensated for using an appropriate Lyapunov-Krasovskii functional. The boundedness of all signals of the closed-loop system as well as the exponential convergence of the underlying tracking errors to an adjustable region are established. The effectiveness of the proposed fuzzy adaptive controller is illustrated throughout simulation results.

MSC:
93C42 Fuzzy control/observation systems
93C35 Multivariable systems, multidimensional control systems
93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
93B12 Variable structure systems
93C15 Control/observation systems governed by ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] A. Boulkroune, M. M’Saad, M. Tadjine, M. Farza, Adaptive fuzzy control for MIMO nonlinear systems with unknown dead-zone, in: Proc. of the Fourth Internat. IEEE Conf. on Intelligent Systems, Varna, Bulgaria, September 2008, pp. 450-455.
[2] Boulkroune, A.; Tadjine, M.; M’saad, 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] Boulkroune, A.; M’Saad, M.; Tadjine, M.; Farza, M., Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction, Fuzzy sets and systems, 161, 797-820, (2010) · Zbl 1217.93086
[4] Boulkroune, A.; Tadjine, M.; M’saad, M.; Farza, M., Adaptive fuzzy controller for non-affine systems with zero dynamics, International journal of systems science, 40, 4, 367-382, (2009) · Zbl 1172.93358
[5] Chang, Y.C., Robust tracking control for nonlinear MIMO systems via fuzzy approaches, Automatica, 36, 1535-1545, (2000) · Zbl 0967.93060
[6] Chekireb, H.; Tadjine, M.; Bouchaffra, D., Direct adaptive fuzzy control of nonlinear system class with applications, Control and intelligent systems, 31, 2, 1-11, (2003) · Zbl 1082.93539
[7] J. Chen, A. Behal, D.M. Dawson, Adaptive output feedback control for a class of MIMO nonlinear systems, in: Proc. of the American Control Conf., Minneapolis, MN, June 2006, pp. 5300-5305.
[8] Costa, R.R.; Hsu, Li.; Imai, A.K.; Kokotovic, P., Lyapunov-based adaptive control of MIMO systems, Automatica, 39, 7, 1251-1257, (2003) · Zbl 1029.93041
[9] Essounbouli, N.; Hamzaoui, A.; Zaytoon, J., An improved robust adaptive fuzzy controller for MIMO systems, Control and intelligent systems, 34, 1, 12-21, (2006) · Zbl 1172.93360
[10] Ge, S.S.; Hong, F.; Lee, T.H., Adaptive neural network control of nonlinear systems with unknown time delays, IEEE transactions on automatic control, 48, 11, 2004-2010, (2003) · Zbl 1364.93392
[11] Ge, S.S.; Hong, F.; Lee, T.H., Adaptive neural control of nonlinear time-delay system with unknown virtual control coefficients, IEEE transactions on systems, man, and cybernetics—part B: cybernetics, 34, 1, 499-516, (2004)
[12] Ge, S.S.; Tee, K.P., Approximation-based control of nonlinear MIMO time-delay systems, Automatica, 43, 31-43, (2007) · Zbl 1137.93042
[13] Golea, N.; Golea, A.; Benmahammed, K., Stable indirect fuzzy adaptive control, Fuzzy sets and systems, 137, 353-366, (2003) · Zbl 1037.93053
[14] Gu, K.; Kharitonov, V.L.; Chen, J., Stability of time-delay systems, (2003), Birkhauser Boston · Zbl 1039.34067
[15] Gutierrez, H.M.; Ro, P.I., Sliding-mode control of a nonlinear-input system: application to a magnetically levitated fast-tool servo, IEEE transactions on industrial electronics, 45, 921-927, (1998)
[16] Hsu, K.-C., Decentralized sliding mode controller for uncertain time-delayed systems with series nonlinearities, ASME journal of dynamic systems, measurement and control, 121, 4, 708-713, (1999)
[17] Hsu, K.-C.; Wang, W.-Y.; Lin, P.-Z., Sliding mode control for uncertain nonlinear systems with multiple inputs containing sector nonlinearities and deadzones, IEEE transactions on systems, man and cybernetic, part-B, 34, 1, 374-380, (2004)
[18] 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 transactions on automatic control, 52, 2, 364-371, (2007) · Zbl 1366.93291
[19] Kharitonov, V.L.; Melchor-Aguilar, D., Lyapunov – krasovskii functionals for additional dynamics, International journal of robust nonlinear control, 13, 793-804, (2003) · Zbl 1034.93033
[20] Kolmanovskii, V.B.; Richard, J., Stability of some linear systems with delays, IEEE transactions on automatic control, 44, 5, 984-989, (1999) · Zbl 0964.34065
[21] 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
[22] Li, H.-X.; Tong, S.C., A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems, IEEE transactions on fuzzy systems, 11, 1, 24-34, (2003)
[23] Niu, Y.; Ho, D.W.C., Design of sliding mode control for nonlinear stochastic systems subject to actuator nonlinearity, IEE proceedings—control theory and applications, 153, 6, 737-744, (2006)
[24] Ordonez, R.; Passino, K.M., Stable multi-input multi-output adaptive fuzzy/neural control, IEEE transactions on fuzzy systems, 7, 3, 345-353, (1999)
[25] Shyu, K.-K.; Liu, W.-J.; Hsu, K.-C., Decentralized variable structure control design for uncertain large scale systems containing a deadzone, IEE proceedings—control theory and applications, 150, 5, 467-475, (2003)
[26] Shyu, K.-K.; Liu, W.-J.; Hsu, K.-C., Design of large-scale time-delayed systems with dead-zone input via variable structure control, Automatica, 41, 1239-1246, (2005) · Zbl 1080.93003
[27] Strang, G., Linear algebra and its applications, (1980), Academic Press New York · Zbl 0463.15001
[28] Sun, Y.; Hsieh, J.; Yang, H., On the stability of uncertain systems with multiple time-varying delays, IEEE transactions on automatic control, 42, 1, 101-105, (1997) · Zbl 0871.93045
[29] 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
[30] Tong, S.C.; Li, H.X., Fuzzy adaptive sliding model control for MIMO nonlinear systems, IEEE transactions on fuzzy systems, 11, 3, 354-360, (2003)
[31] 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
[32] Wang, M.; Chen, B.; Liu, K.; Liu, X.; Zhang, S., Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients, Information sciences, 178, 4326-4340, (2008) · Zbl 1148.93324
[33] Wang, L.X., Adaptive fuzzy systems and control: design and stability analysis, (1994), Prentice-Hall Englewood Cliffs, NJ
[34] 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
[35] Zhang, T.P.; Yi, Y., Adaptive fuzzy control for a class of MIMO nonlinear systems with unknown dead-zones, Acta automatica sinica, 33, 1, 96-99, (2007)
[36] 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. of the IEEE Internat. Conf. on Control Applications, Taipei, Taiwan, September 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.