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)
Design of sliding surface for mismatched uncertain systems to achieve asymptotical stability. (English) Zbl 1201.93108
Summary: The design of an adaptive Sliding Mode Control (SMC) scheme is proposed in this paper for stabilizing a class of dynamic systems with matched and mismatched perturbations. Two methods for designing a novel sliding surface function are introduced first. By utilizing a pseudocontrol input in the sliding surface function, one cannot only suppress the mismatched perturbations in the sliding mode, but also obtain the property of asymptotic stability. Then a sliding mode controller is designed to drive the controlled systems to the designated sliding surface in a finite time. Adaptive mechanism is also embedded in the controller as well as in the sliding surface function designed from the second method to overcome the perturbations, so that the informations of upper bound of perturbations are not required. An application of flight control and experimental results of controlling a servomotor are also given for demonstrating the applicability of the proposed control scheme.
MSC:
93D20Asymptotic stability of control systems
93C40Adaptive control systems
93B12Variable structure systems
References:
[1]Utkin, V. I.: Variable structure systems with sliding modes, IEEE trans. Automat. control 22, No. 2, 212-221 (1977) · Zbl 0382.93036 · doi:10.1109/TAC.1977.1101446
[2]Barmish, B. R.; Leitmann, G.: On ultimate boundedness control of uncertain systems in the absence of matching assumptions, IEEE trans. Automat. control 27, No. 1, 153-158 (1982) · Zbl 0469.93043 · doi:10.1109/TAC.1982.1102862
[3]Singh, S. N.; Antônio, A. R. Coelho: Nonlinear control of mismatched uncertain linear systems and application to control of aircraft, J. dyn. Syst. meas. Control trans. ASME 106, No. 3, 203-210 (1984) · Zbl 0557.93038 · doi:10.1115/1.3149673
[4]Liao, T. L.; Fu, L. C.; Hsu, C. F.: Output tracking control of nonlinear systems with mismatched uncertainties, Syst. control lett. 18, No. 1, 39-47 (1992) · Zbl 0743.93053 · doi:10.1016/0167-6911(92)90106-3
[5]Spurgeon, S. K.; Davies, R.: A nonlinear control strategy for robust sliding mode performance in the absence of mismatched uncertainty, Int. J. Control 57, No. 5, 1107-1123 (1993) · Zbl 0772.93013 · doi:10.1080/00207179308934433
[6]J. Hu, J. Chu, H. Su, SMVSC for a class of time-delay uncertain systems with mismatching uncertainties, IEE Proceeding – Control Theory and Applications, vol. 147(6), 2000, pp. 687 – 693.
[7]Tao, C. W.; Chan, M. L.; Lee, T. T.: Adaptive fuzzy sliding mode controller for linear systems with mismatched time-varying uncertainties, IEEE trans. Syst. man cybern. Part B cybern. 33, No. 2, 283-294 (2003)
[8]Kwan, C. M.: Sliding mode control of linear systems with mismatched uncertainties, Automatica 31, No. 2, 303-307 (1995) · Zbl 0821.93021 · doi:10.1016/0005-1098(94)00093-X
[9]Choi, H. H.: An explicit formula of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties, Automatica 34, No. 8, 1015-1020 (1998) · Zbl 1040.93506 · doi:10.1016/S0005-1098(98)00042-9
[10]Choi, H. H.: Variable structure output feedback control design for a class of uncertain dynamic systems, Automatica 38, No. 2, 335-341 (2002) · Zbl 0991.93021 · doi:10.1016/S0005-1098(01)00211-4
[11]Choi, H. H.: An LMI-based switching surface design method for a class of mismatched uncertain systems, IEEE trans. Automat. control 48, No. 9, 1634-1638 (2003)
[12]Chan, M. L.; Tao, C. W.; Lee, T. T.: Sliding mode controller for linear systems with mismatched time-varying uncertainties, J. franklin inst. Eng. appl. Math. 337, No. 2, 105-115 (2000) · Zbl 0981.93012 · doi:10.1016/S0016-0032(00)00011-9
[13]Kim, K. S.; Park, Y.; Oh, S. H.: Designing robust sliding hyperplanes for parametric uncertain systems: a Riccati approach, Automatica 36, No. 7, 1041-1048 (2000) · Zbl 0955.93005 · doi:10.1016/S0005-1098(00)00014-5
[14]Tsai, Y. W.; Shyu, K. K.; Chang, K. C.: Decentralized variable structure control for mismatched uncertain large-scale systems: a new approach, Syst. control lett. 43, No. 2, 117-125 (2001) · Zbl 0974.93014 · doi:10.1016/S0167-6911(01)00081-0
[15]Shyu, K. K.; Tsai, Y. W.; Lai, C. K.: A dynamic output feedback controllers for mismatched uncertain variable structure systems, Automatica 37, No. 5, 775-779 (2001) · Zbl 0981.93010
[16]Cao, W. J.; Xu, J. X.: Nonlinear integral-type sliding surface for both matched and mismatched uncertain systems, IEEE trans. Automat. control 49, No. 8, 1355-1360 (2004)
[17]Yoo, D. S.; Chung, M. J.: A variable structure control with simple adaptation laws for upper bounds on the norm of the uncertainties, IEEE trans. Automat. control 37, No. 6, 860-865 (1992) · Zbl 0760.93014 · doi:10.1109/9.256348
[18]Chou, C. -H.; Cheng, C. C.: Design of adaptive variable structure controllers for perturbed time-varying state delay systems, J. franklin inst. Eng. appl. Math. 388, No. 1, 35-46 (2001) · Zbl 0966.93101 · doi:10.1016/S0016-0032(00)00070-3
[19]Chou, C. -H.; Cheng, C. C.: A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems, IEEE trans. Automat. control 48, No. 7, 1123-1127 (2003)
[20]Hung, J. Y.; Gao, W.; Hung, J. C.: Variable structure control: a survey, IEEE trans. Automat. control 40, No. 1, 2-22 (1993)
[21]Leon, S. J.: Linear algebra with applications, (1999)
[22]El-Ghezawi, O. M. E.; Zinober, A. S. I.; Billings, S. A.: Analysis and design of variable structure systems using a geometric approach, Int. J. Control 38, No. 3, 657-671 (1983) · Zbl 0538.93035 · doi:10.1080/00207178308933100
[23]&zdot, S. H.; Ak; Hui, S.: On variable structure output feedback controllers for uncertain dynamic systems, IEEE trans. Automat. control 38, No. 10, 1509-1512 (1993)
[24]Khalil, H. K.: Nonlinear systems, (2000)
[25]Slotine, J. J. E.; Li, W.: Applied nonlinear control, (1991) · Zbl 0753.93036
[26]Shyu, K. K.; Tsai, Y. W.; Lai, C. K.: Stability regions estimation for mismatched uncertain variable structure systems with bounded controllers, Electron. lett. 35, No. 16, 1388-1390 (1999)