zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

93C42Fuzzy control systems
93C35Multivariable systems, multidimensional control systems
93C40Adaptive control systems
93C10Nonlinear control systems
93B12Variable structure systems
93C15Control systems governed by ODE
Full Text: DOI
[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 · doi:10.1016/j.fss.2007.08.015
[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 · doi:10.1016/j.fss.2009.04.011
[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, No. 4, 367-382 (2009) · Zbl 1172.93358 · doi:10.1080/00207720802436919
[5] Chang, Y. C.: Robust tracking control for nonlinear MIMO systems via fuzzy approaches, Automatica 36, 1535-1545 (2000) · Zbl 0967.93060 · doi:10.1016/S0005-1098(00)00083-2
[6] Chekireb, H.; Tadjine, M.; Bouchaffra, D.: Direct adaptive fuzzy control of nonlinear system class with applications, Control and intelligent systems 31, No. 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, No. 7, 1251-1257 (2003) · Zbl 1029.93041 · doi:10.1016/S0005-1098(03)00085-2
[9] Essounbouli, N.; Hamzaoui, A.; Zaytoon, J.: An improved robust adaptive fuzzy controller for MIMO systems, Control and intelligent systems 34, No. 1, 12-21 (2006) · Zbl 1172.93360 · doi:10.2316/Journal.201.2006.1.201-1350
[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, No. 11, 2004-2010 (2003)
[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, No. 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 · doi:10.1016/j.automatica.2006.08.003
[13] Golea, N.; Golea, A.; Benmahammed, K.: Stable indirect fuzzy adaptive control, Fuzzy sets and systems 137, 353-366 (2003) · Zbl 1037.93053 · doi:10.1016/S0165-0114(02)00279-8
[14] Gu, K.; Kharitonov, V. L.; Chen, J.: Stability of time-delay systems, (2003) · 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, No. 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, No. 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, No. 2, 364-371 (2007)
[19] Kharitonov, V. L.; Melchor-Aguilar, D.: Lyapunov -- Krasovskiĭ functionals for additional dynamics, International journal of robust nonlinear control 13, 793-804 (2003) · Zbl 1034.93033 · doi:10.1002/rnc.845
[20] Kolmanovskii, V. B.; Richard, J.: Stability of some linear systems with delays, IEEE transactions on automatic control 44, No. 5, 984-989 (1999) · Zbl 0964.34065 · doi:10.1109/9.763213
[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 · doi:10.1016/j.fss.2004.10.009
[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, No. 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, No. 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, No. 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, No. 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 · doi:10.1016/j.automatica.2005.03.004
[27] Strang, G.: Linear algebra and its applications, (1980) · Zbl 0548.15004
[28] Sun, Y.; Hsieh, J.; Yang, H.: On the stability of uncertain systems with multiple time-varying delays, IEEE transactions on automatic control 42, No. 1, 101-105 (1997) · Zbl 0871.93045 · doi:10.1109/9.553692
[29] Tong, S. C.; Tang, J.; Wang, T.: Fuzzy adaptive control of multivariable nonlinear systems, Fuzzy sets and systems 111, No. 2, 153-167 (2000) · Zbl 0976.93049 · doi:10.1016/S0165-0114(98)00052-9
[30] Tong, S. C.; Li, H. X.: Fuzzy adaptive sliding model control for MIMO nonlinear systems, IEEE transactions on fuzzy systems 11, No. 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, No. 2, 285-299 (2005) · Zbl 1082.93032 · doi:10.1016/j.fss.2005.06.011
[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 · doi:10.1016/j.ins.2008.07.008
[33] Wang, L. X.: Adaptive fuzzy systems and control: design and stability analysis, (1994)
[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, No. 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, No. 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.