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 output feedback control for MIMO nonlinear systems. (English) Zbl 1082.93032
Summary: Two observer-based adaptive fuzzy output feedback control schemes are presented for a class of uncertain continuous-time multi-input--multi-output (MIMO) nonlinear dynamics systems whose states are not available. Within these schemes, fuzzy logic systems are employed to approximate the plant’s unknown nonlinear functions and then the state observer is designed for estimating the states of the plant, upon which a fuzzy adaptive output feedback controller is firstly investigated. In order to overcome the controller singularity problem and relax the requirement of bounding parameter values, a second modified fuzzy adaptive output feedback controller is proposed by using a regularized inverse and a robustifying control term. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis, so that convergence to zero of tracking errors and boundedness of all signals in the closed-loop system can be guaranteed. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.

93C42Fuzzy control systems
93C40Adaptive control systems
Full Text: DOI
[1] Chang, Y. C.: Robust tracking control for nonlinear MIMO systems via fuzzy approaches. Automatica 36, 1535-1545 (2000) · Zbl 0967.93060
[2] 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 3, No. 4, 32-43 (1994)
[3] Kanellakopoulos, I.; Kokotovic, P. V.; Morse, A. S.: Systematic design of adaptive controllers for feedback linearizable systems. IEEE trans. Automat. control 36, 1241-1253 (1991) · Zbl 0768.93044
[4] Krstic, M.; Kanellakopoulos, I.; Kokotovic, P. V.: Nonlinear and adaptive control design. (1995)
[5] Li, H. X.; Tong, S. C.: A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems. IEEE trans. Fuzzy systems 11, No. 1, 24-35 (2003)
[6] Ordonez, R.; Passino, K. M.: Stable multi-output adaptive fuzzy/neural control. IEEE trans. Fuzzy systems 4, 32-43 (1999)
[7] Sastry, S. S.; Bodson, M.: Adaptive control: stability, convergence, and robustness. (1989) · Zbl 0721.93046
[8] Sastry, S. S.; Isidori, A.: Adaptive control of a class of nonlinear systems. IEEE trans. Automat. control 34, 1123-1131 (1989) · Zbl 0693.93046
[9] Slotine, J. E.; Li, W.: Applied nonlinear control. (1991) · Zbl 0753.93036
[10] 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) · Zbl 0842.93036
[11] Su, C. Y.; Stepanenko, Y.: Adaptive control of a class of nonlinear systems with fuzzy logic. IEEE trans. Fuzzy systems 3, 339-359 (1994)
[12] 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
[13] 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
[14] Tong, S. C.; Wang, T.; Tang, J. T.: Fuzzy adaptive output tracking control of nonlinear systems. Fuzzy sets and systems 111, 169-182 (2000) · Zbl 0976.93050
[15] Wang, L. X.: Stable adaptive fuzzy control of nonlinear systems. IEEE trans. Fuzzy systems 1, No. 2, 32-43 (1993)
[16] Wang, L. X.: Adaptive fuzzy systems and control: design and stability. (1994)
[17] Leu, Yin-Guang; Lee, Tsu-Tian; Wang, Wei-Yen: Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems. IEEE trans. Systems man cybernet. 29, 583-591 (1999)
[18] Zhang, H. G.; Bie, Z. B.: Adaptive fuzzy control of MIMO nonlinear systems. Fuzzy sets and systems 115, 191-204 (2000) · Zbl 0960.93024