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)
Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction. (English) Zbl 1205.93136
Summary: A direct fuzzy adaptive robust control approach is proposed for a class of SISO nonlinear systems with completely unknown virtual control directions, unknown nonlinearities, unmodeled dynamics and dynamic disturbances. In the backstepping recursive design, fuzzy logic systems are employed to approximate the combined nonlinear uncertainties, a dynamic signal and Nussbaum gain technique are introduced into the control scheme to dominate the dynamic uncertainties and solve the unknown signs of virtual control directions, respectively. It is proved that the proposed robust fuzzy adaptive scheme can guarantee that all signals in the closed-loop system are semi-globally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated via three examples.
93D21Adaptive or robust stabilization
93C10Nonlinear control systems
93C42Fuzzy control systems
93C40Adaptive control systems
[1]Boulkroune, A.; Tadjine, M.; Saad, M. M.; Farza, M.: How to design a fuzzy adaptive controller 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
[2]Boulkroune, A.; Tadjine, M.; Msaad, M.; Farza, M.: Adaptive fuzzy controller for nonaffine systems with zero dynamics, International journal of systems sciences 40, 367-382 (2009) · Zbl 1172.93358 · doi:10.1080/00207720802436919
[3]Boulkroune, A.; Tadjine, M.; Msaad, M.; Farza, M.: Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction, Fuzzy sets and systems 161, No. 6, 797-820 (2010) · Zbl 1217.93086 · doi:10.1016/j.fss.2009.04.011
[4]Chen, B.; Liu, X. P.: Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes, IEEE transactions on fuzzy systems 13, No. 6, 832-847 (2005)
[5]Chen, B.; Liu, X. P.; Tong, S. C.: Adaptive fuzzy output tracking control of MIMO nonlinear uncertain systems, IEEE transactions on fuzzy systems 15, No. 2, 287-300 (2007)
[6]Chen, B.; Liu, X. P.; Liu, K. F.; Shi, P.; Lin, C.: Direct adaptive fuzzy control for nonlinear systems with time-varying delays, Information sciences 180, No. 5, 776-792 (2010) · Zbl 1182.93074 · doi:10.1016/j.ins.2009.11.004
[7]Chen, C. Y.; Li, T. H. S.; Yeh, Y. C.: EP-based kinematic control and adaptive fuzzy sliding-mode dynamic control for wheeled mobile robots, Information sciences 179, 180-195 (2009) · Zbl 1158.93356 · doi:10.1016/j.ins.2008.09.012
[8]Chen, C. S.: Dynamic structure adaptive neural fuzzy control for MIMO uncertain nonlinear systems, Information sciences 179, No. 15, 2676-2688 (2009) · Zbl 1165.93322 · doi:10.1016/j.ins.2009.03.015
[9]Dawson, D. M.; Carroll, J. J.; Schneider, M.: Integrator backstepping control of a rush DC motor turning a robotic load, IEEE transactions on control systems technology 2, 233-244 (1994)
[10]Ding, Z. T.; Ye, X. D.: A flat-zone modification for robust adaptive control of nonlinear output feedback systems with unknown high-frequency gains, IEEE transactions on automatic control 47, No. 2, 358-363 (2002)
[11]Ge, S. S.; Wang, J.: Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems, IEEE transactions on neural networks 13, No. 6, 1409-1419 (2002)
[12]Ge, S. S.; Zhang, J.: Neural-network control of nonaffine nonlinear system with zero dynamics by state and output feedback, IEEE transactions on neural networks 14, 900-918 (2003)
[13]Hwang, G. H.; Kim, D. W.; Lee, J. H.; An, Y. J.: Design of fuzzy power system stabilizer using adaptive evolutionary algorithm, Engineering applications of artificial intelligence 21, No. 1, 86-96 (2008)
[14]Ioannou, P. A.; Sun, J.: Robust adaptive control, (1996) · Zbl 0839.93002
[15]Jagannnathan, S.; Lewis, F. L.: Robust backstepping control of a class of nonlinear systems using fuzzy logic, Information sciences 123, 223-240 (2000) · Zbl 0953.93522 · doi:10.1016/S0020-0255(99)00128-0
[16]Jiang, Z. P.; Parly, L.: Technical results for the study of robustness of Lagrange stability, Systems and control letters 23, 67-78 (1994) · Zbl 0800.93997 · doi:10.1016/0167-6911(94)90082-5
[17]Jiang, Z. P.; Praly, L.: Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties, Automatica 34, No. 7, 825-840 (1998) · Zbl 0951.93042 · doi:10.1016/S0005-1098(98)00018-1
[18]Kaloust, J.; Qu, Z.: Continuous robust control design for nonlinear uncertain systems without a priori knowledge of control direction, IEEE transactions on automatic control 40, No. 2, 276-282 (1995) · Zbl 0825.93606 · doi:10.1109/9.341792
[19]Kanellakopopoulos, I.; Kokotovic, P. V.; Morse, A. S.: Systematic design of adaptive controllers for feedback linearizable systems, IEEE transactions on automatic control 36, No. 11, 1241-1253 (1991) · Zbl 0768.93044 · doi:10.1109/9.100933
[20]Kristic, M.; Kanellakopoulos, I.; Kokotovic, P. V.: Nonlinear and adaptive control design, (1995)
[21]Lin, W.; Qian, C. J.; Huang, X. Q.: Disturbance attenuation of a class of non-linear systems via output feedback, International journal of robust and nonlinear control 13, 1359-1369 (2003) · Zbl 1046.93034 · doi:10.1002/rnc.859
[22]Liu, Y. S.; Li, X. Y.: Decentralized robust adaptive control of nonlinear systems with unmodeled dynamics, IEEE transactions on automatic control 47, No. 5, 848-856 (2002)
[23]E.H. Mamdani, S. Assilian, Applications of fuzzy algorithms for control of simple dynamic plant, in: Proc. Inst. Electr. Eng. D, vol. 121, 1974, pp. 1585 – 1588.
[24]Mudgett, D. R.; Morse, A. S.: Adaptive stabilization of linear systems with unknown high frequency gain, IEEE transactions on automatic control 30, No. 6, 549-554 (1985) · Zbl 0573.93037 · doi:10.1109/TAC.1985.1104006
[25]Nussbaum, R. D.: Some remarks on the conjecture in parameter adaptive control, Systems and control letters 3, No. 5, 243-246 (1983) · Zbl 0524.93037 · doi:10.1016/0167-6911(83)90021-X
[26]Praly, L.; Jiang, Z. P.: Linear output feedback with dynamic high gain for nonlinear systems, Systems and control letters 53, 107-116 (2004) · Zbl 1157.93494 · doi:10.1016/j.sysconle.2004.02.025
[27]Precup, R. E.; Preitl, S.: Optimisation criteria in development of fuzzy controllers with dynamics, Engineering applications of artificial intelligence 17, 661-674 (2004)
[28]Qian, C. J.; Lin, W.: Output feedback control of a class of nonlinear systems: a non-separation principle paradigm, IEEE transactions on automatic control 47, No. 10, 1710-1715 (2002)
[29]Sanchez, E. N.; Becerra, H. M.; Velez, C. M.: Combining fuzzy, PID and regulation control for an autonomous mini-helicopter, Information sciences 177, 1999-2022 (2007)
[30]Seto, D.; Annaswamy, A. M.; Baillieul, J.: Adaptive control of nonlinear systems with triangular structure, IEEE transactions on automatic control 39, No. 7, 1411-1428 (1994) · Zbl 0806.93034 · doi:10.1109/9.299624
[31]Tong, S. C.; Li, Y. M.; Shi, P.: Fuzzy adaptive backstepping robust control for SISO nonlinear systems with dynamic uncertainties, Information sciences 179, 1319-1332 (2009) · Zbl 1156.93357 · doi:10.1016/j.ins.2009.01.002
[32]Tong, S. C.; He, X. L.; Li, Y. M.: Direct adaptive fuzzy backstepping robust control for single input and single output uncertain nonlinear systems using small-gain approach, Information sciences 180, No. 9, 738-1758 (2010)
[33]Wang, L. X.: Adaptive fuzzy systems and control: design and stability analysis, (1994)
[34]Wang, M.; Chen, B.: 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
[35]Wang, W. Y.; Chan, M. L.; Lee, T. T.; Liu, C. H.: Adaptive fuzzy control for strict-feedback canonical nonlinear systems with H tracking performance, IEEE transactions on systems, man, and cybernetics – part B 31, No. 6, 878-885 (2001)
[36]Wu, Z. J.; Xie, X. J.; Shi, P.: Robust adaptive output-feedback control for nonlinear systems with output unmodeled dynamics, International journal robust nonlinear control 18, 1162-1187 (2008)
[37]Yang, Y. S.; Zhou, C. J.: Robust adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems via small-gain approach, Information sciences 170, 211-234 (2005) · Zbl 1068.93037 · doi:10.1016/j.ins.2004.02.022
[38]Ye, X. D.: Adaptive nonlinear output-feedback control with unknown high-frequency gain sign, IEEE transactions on automatic control 46, No. 1, 112-115 (2001) · Zbl 1062.93517 · doi:10.1109/9.898701
[39]Zhao, Y. N.; Collins, E. G.: Fuzzy PI control design for an industrial weigh belt feeder, IEEE transactions on fuzzy systems 11, No. 3, 311-319 (2003)
[40]Zhou, S. S.; Feng, G.; Feng, C. B.: Robust control for a class of uncertain nonlinear systems: adaptive fuzzy approach based on backstepping, Fuzzy sets and systems 151, No. 1, 1-20 (2005) · Zbl 1142.93378 · doi:10.1016/j.fss.2004.05.008
[41]Zou, A. M.; Hou, Z. G.: Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach, IEEE transactions on fuzzy systems 16, No. 4, 886-897 (2008)
[42]Liu, Y. J.; Wang, W.: Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems, Information sciences 177, 3901-3917 (2007) · Zbl 1121.93037 · doi:10.1016/j.ins.2007.03.005