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)
Fuzzy rule-based combination of linear and switching state-feedback controllers. (English) Zbl 1082.93027
Summary: This paper presents a fuzzy rule-base combined controller, which is a fuzzy rule-based combination of linear and switching state-feedback controllers, for nonlinear systems subject to parameter uncertainties. The switching state-feedback controller is employed to drive the system states toward the origin. When the system state approaches the origin, the linear state-feedback controller will gradually replace the switching state-feedback controller. The smooth transition between the linear and switching state-feedback controllers is governed by the fuzzy rules. By using the fuzzy rule-based combination technique, the proposed fuzzy rule-base combined controller integrates the advantages of both the linear and switching state-feedback controllers but eliminates their disadvantages. As a result, the proposed fuzzy controller provides good performance during the transient period and the chattering effect is removed when the system state approaches the origin. Stability conditions will be derived to guarantee the system stability. Furthermore, a saturation function is employed to replace the switching component to alleviate the chattering during the transient period. By using the proposed fuzzy rule-based combination technique, the steady state error introduced by the saturation function can be eliminated. Application examples will be given to show the merits of the proposed approach.

MSC:
93C42Fuzzy control systems
93B50Synthesis problems
Software:
Genocop
WorldCat.org
Full Text: DOI
References:
[1] Chang, J.; Kuo, H.: Decoupled fuzzy sliding-mode control. IEEE trans. Fuzzy systems 6, No. 3, 426-435 (1998)
[2] Decarlo, R. A.; Zak, S. H.; Matthews, G. P.: Variable structure control of nonlinear multivariable systems: a tutorial. Proc. IEEE 76, No. 3, 212-232 (1988)
[3] Feng, G.: Approaches to quadratic stabilization of uncertain fuzzy dynamic systems. IEEE trans. Circuits systems I: fund. Appl. 48, No. 6, 760-769 (2001) · Zbl 0992.93045
[4] Guo, Y.; Woo, P. Y.: An adaptive fuzzy sliding mode controller for robotic manipulators. IEEE trans. Systems man cybernetic part B 33, No. 2, 149-159 (2003)
[5] Johansson, M.; Rantzer, A.; årzén, K. E.: Piecewise quadratic stability of fuzzy systems. IEEE trans. Fuzzy systems 7, No. 6, 713-722 (1999)
[6] Kim, E.: New approaches to relaxed quadratic stability conditions of fuzzy control systems. IEEE trans. Fuzzy systems 8, No. 5, 523-534 (2000)
[7] Lam, H. K.; Leung, F. H. F.; Lee, Y. S.: Design of a switching controller for nonlinear systems with unknown parameters based on a fuzzy logic approach. IEEE trans. Systems man cybernetics part B: cybernetics 34, No. 2, 1068-1074 (2004)
[8] Lam, H. K.; Leung, F. H. F.; Tam, P. K. S.: A switching controller for uncertain nonlinear systems. IEEE control systems mag. 22, No. 1, 7-14 (2002)
[9] Lam, H. K.; Leung, F. H. F.; Tam, P. K. S.: Design and stability analysis of fuzzy model based nonlinear controller for nonlinear systems using genetic algorithm. IEEE trans. Systems man cybernetics part B: cybernetics 33, No. 2, 250-257 (2003)
[10] Leung, F. H. F.; Lam, H. K.; Ling, S. H.; Tam, P. K. S.: Optimal and stable fuzzy controllers for uncertain nonlinear systems based on an improved genetic algorithm. IEEE trans. Indust. electron. 51, No. 1, 172-182 (2004)
[11] Leung, F. H. F.; Lam, H. K.; Tam, P. K. S.: Design of fuzzy controllers for uncertain nonlinear systems using stability and robustness analyses. System control lett. 35, No. 4, 237-283 (1998) · Zbl 0909.93040
[12] Michalewicz, Z.: Genetic algorithm + data structures = evolution programs. (1994) · Zbl 0818.68017
[13] Slotine, J. J. E.; Li, W.: Applied nonlinear control. (1991) · Zbl 0753.93036
[14] Spong, M. W.; Khorsani, K.; Kokotovic, P. V.: An integral manifold approach to the feedback control of flexible joint robots. IEEE J. Robot. autom. 3, No. 4, 291-300 (1987)
[15] Sugeno, M.; Kang, G. T.: Structure identification of fuzzy model. Fuzzy sets and systems 28, 15-33 (1988) · Zbl 0652.93010
[16] Sun, F. C.; Sun, Z. Q.; Fend, G.: An adaptive fuzzy controller based on sliding mode for robot manipulator. IEEE trans. Systems man cybernetic part B 29, No. 4, 661-667 (1999)
[17] Takagi, T.; Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE trans. Systems man cybernetics 15, 116-132 (1985) · Zbl 0576.93021
[18] Tanaka, K.; Hori, T.; Wang, H. O.: A multiple Lyapunov function approach to stabilization of fuzzy control systems. IEEE trans. Fuzzy systems 11, No. 4, 582-589 (2003)
[19] Tanaka, K.; Ikeda, T.; Wang, H. O.: Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stability, H$\infty $ control theory, and linear matrix inequalities. IEEE trans. Fuzzy system 4, No. 1, 1-13 (1996)
[20] Tanaka, K.; Ikeda, T.; Wang, H. O.: Fuzzy regulator and fuzzy observer: relaxed stability conditions and LMI-based designs. IEEE trans. Fuzzy systems 6, No. 2, 250-265 (1998)
[21] Tanaka, K.; Sugeno, M.: Stability analysis and design of fuzzy control systems. Fuzzy sets and systems 45, 135-156 (1992) · Zbl 0758.93042
[22] Ting, C. S.; Li, T. H.; Kung, F. C.: An approach to systematic design of the fuzzy control system. Fuzzy sets and systems 77, 151-166 (1996)
[23] Vidyasagar, M.: Nonlinear systems analysis. (1993) · Zbl 0900.93132
[24] Wang, H. O.; Tanaka, K.; Griffin, M. F.: An approach to fuzzy control of nonlinear systems: stability and the design issues. IEEE trans. Fuzzy systems 4, No. 1, 14-23 (1996)
[25] Wang, L. X.: Adaptive fuzzy systems and control: design and stability analysis. (1994)
[26] Wang, W. J.; Lee, J. L.: Hitting time reduction and chattering attenuation in multi-input variable structure systems. Control theory adv. Technol. 9, No. 2, 491-500 (1993)
[27] Wang, W. J.; Yan, S. F.; Chiu, C. H.: Flexible stability criteria for a linguistic fuzzy dynamic system. Fuzzy sets and systems 105, No. 1, 63-80 (1999) · Zbl 0933.93052
[28] &zdot, S. H.; Ak: Stabilizing fuzzy system models using linear controllers. IEEE trans. Fuzzy systems 7, No. 2, 236-240 (1999)
[29] Zhang, D. Q.; Panda, S. K.: Chattering-free and fast-response sliding mode controller. IEE proc. Control theory appl. 146, No. 2, 171-177 (1999)