# zbMATH — the first resource for mathematics

##### Examples
 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.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 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)
Observer-based fuzzy adaptive control for strict-feedback nonlinear systems. (English) Zbl 1175.93135
Summary: A new fuzzy adaptive control approach is developed for a class of single-input single-output strict-feedback nonlinear systems with unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is introduced for state estimation as well as for system identification. Under the framework of the backstepping design, fuzzy adaptive output feedback control is constructed recursively. It is proven that the proposed fuzzy adaptive control approach guarantees the semi-global boundedness property for all the signals and the tracking error to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.
##### MSC:
 93C42 Fuzzy control systems 93C40 Adaptive control systems 93C10 Nonlinear control systems 93B52 Feedback control
##### References:
 [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] Chen, B.; Liu, X. P.: Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping and application to chemical processes, IEEE trans. Fuzzy systems 13, 832-847 (2005) [3] Chen, B.; Liu, X. P.; Tong, S. C.: Fuzzy approximate disturbance decoupling of MIMO nonlinear systems by backstepping approach, Fuzzy sets and systems 158, 1097-1125 (2007) · Zbl 1113.93068 · doi:10.1016/j.fss.2006.12.012 [4] Chen, B. S.; Lee, C. H.; Chang, Y. C.: H$\infty$ tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach, IEEE trans. Fuzzy systems 4, 32-43 (1996) [5] Chiu, C. S.: Mixed feedforward/feedback based adaptive fuzzy control for a class of MIMO nonlinear systems, IEEE trans. Fuzzy systems 14, 716-727 (2006) [6] Golea, N.; Golea, A.; Barra, K.: Observer-based adaptive control of robot manipulators: fuzzy systems approach, Appl. comput. 8, 778-787 (2008) [7] Golea, N.; Golea, A.; Benmahammed, K.: Stable indirect fuzzy adaptive control, Fuzzy sets and systems 127, 353-366 (2003) · Zbl 1037.93053 · doi:10.1016/S0165-0114(02)00279-8 [8] Hsu, F. Y.; Fu, L. C.: A novel adaptive fuzzy variable structure control for a class of nonlinear uncertain systems via backstepping, Fuzzy sets and systems 22, 83-106 (2001) · Zbl 0991.93064 · doi:10.1016/S0165-0114(00)00068-3 [9] Jagannnathan, S.; Lewis, F. L.: Robust backstepping control of a class of nonlinear systems using fuzzy logic, Inform. sci. 123, 223-240 (2000) · Zbl 0953.93522 · doi:10.1016/S0020-0255(99)00128-0 [10] Kristic, M.; Kanellakopoulos, I.; Kokotovic, P. V.: Nonlinear and adaptive control design, (1995) [11] Leu, Y. G.; Wang, W. Y.: Observer-based adaptive fuzzy – neural control for unknown nonlinear dynamical systems, IEEE trans. Systems man cybernet. 29, 583-591 (1999) [12] Li, H. X.; Tong, S. C.: A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems, IEEE trans. Fuzzy systems 11, 24-34 (2003) [13] Ordones, R.; Passino, K. M.: Stable multi-input multi-output adaptive fuzzy/neural control, IEEE trans. Fuzzy systems 7, 345-353 (1999) [14] Spooner, J. T.; Passino, K. M.: Stable adaptive control of a class of nonlinear systems and neural network, IEEE trans. Fuzzy systems 4, 339-359 (1996) [15] Sue, C. Y.; Stepanenko, Y.: Adaptive control of a class of nonlinear systems with fuzzy logic, IEEE trans. Fuzzy systems 2, 285-294 (1994) [16] Tong, S. C.; Chai, T. Y.: Fuzzy adaptive control for a class of nonlinear systems, Fuzzy sets and systems 101, 31-39 (1999) · Zbl 0952.93077 · doi:10.1016/S0165-0114(97)00055-9 [17] Tong, S. C.; Li, H. X.; Wang, W.: Observer-based adaptive fuzzy control for SISO nonlinear systems, Fuzzy sets and systems 148, 355-376 (2004) · Zbl 1057.93029 · doi:10.1016/j.fss.2003.11.017 [18] Tong, S. C.; Li, Y. M.: Direct adaptive fuzzy backstepping control for a class nonlinear systems, Internat. J. Innovative comput. Informat. control 3, 887-896 (2007) [19] Tong, S. C.; Tang, J. T.; Wang, T.: Fuzzy adaptive control of multivariable nonlinear systems, Fuzzy sets and systems 111, 153-167 (2000) · Zbl 0976.93049 · doi:10.1016/S0165-0114(98)00052-9 [20] Wang, L. X.: Adaptive fuzzy systems and control: design and stability analysis, (1994) [21] Wang, M.; Chen, B.: Direct adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems, Fuzzy sets and systems 158, 2655-2670 (2007) · Zbl 1133.93350 · doi:10.1016/j.fss.2007.06.001 [22] Wang, W. Y.; Leu, Y. G.; Lee, T. T.: Output-feedback control of nonlinear systems using direct adaptive fuzzy – neural controller, Fuzzy sets and systems 140, 341-358 (2003) · Zbl 1032.93541 · doi:10.1016/S0165-0114(02)00519-5 [23] Yang, Y. C.: Robust tracking control of nonlinear MIMO systems via fuzzy approaches, Automatica 36, 1535-1545 (2000) · Zbl 0967.93060 · doi:10.1016/S0005-1098(00)00083-2 [24] Yang, Y. S.; Feng, G.; Ren, J. S.: A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems, IEEE trans. Systems man cybernet. Part A: systems humans 34, 406-420 (2004) [25] Yang, Y. S.; Zhou, C. J.: Adaptive fuzzy H$\infty$ stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach, IEEE trans. Fuzzy systems 13, 104-114 (2005) [26] 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, 1-20 (2005) · Zbl 1142.93378 · doi:10.1016/j.fss.2004.05.008