LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems

Chaouki Mnasri; Moncef Gasmi

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 4, page 605-615
  • ISSN: 1641-876X

Abstract

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Integral sliding mode design is considered for a class of uncertain systems in the presence of mismatched uncertainties in both state and input matrices, as well as norm-bounded nonlinearities and external disturbances. A sufficient condition for the robust stability of the sliding manifold is derived by means of linear matrix inequalities. The initial existence of the sliding mode is guaranteed by the proposed control law. The improvement of the proposed control scheme performances, such as chattering elimination and estimation of norm bounds of uncertainties, is then considered with the application of an adaptive fuzzy integral sliding mode control law. The validity and efficiency of the proposed approaches are investigated through a sixth order uncertain mechanical system.

How to cite

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Chaouki Mnasri, and Moncef Gasmi. "LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems." International Journal of Applied Mathematics and Computer Science 21.4 (2011): 605-615. <http://eudml.org/doc/208073>.

@article{ChaoukiMnasri2011,
abstract = {Integral sliding mode design is considered for a class of uncertain systems in the presence of mismatched uncertainties in both state and input matrices, as well as norm-bounded nonlinearities and external disturbances. A sufficient condition for the robust stability of the sliding manifold is derived by means of linear matrix inequalities. The initial existence of the sliding mode is guaranteed by the proposed control law. The improvement of the proposed control scheme performances, such as chattering elimination and estimation of norm bounds of uncertainties, is then considered with the application of an adaptive fuzzy integral sliding mode control law. The validity and efficiency of the proposed approaches are investigated through a sixth order uncertain mechanical system.},
author = {Chaouki Mnasri, Moncef Gasmi},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {adaptive fuzzy control; integral sliding mode; LMI; mismatched uncertainties},
language = {eng},
number = {4},
pages = {605-615},
title = {LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems},
url = {http://eudml.org/doc/208073},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Chaouki Mnasri
AU - Moncef Gasmi
TI - LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 4
SP - 605
EP - 615
AB - Integral sliding mode design is considered for a class of uncertain systems in the presence of mismatched uncertainties in both state and input matrices, as well as norm-bounded nonlinearities and external disturbances. A sufficient condition for the robust stability of the sliding manifold is derived by means of linear matrix inequalities. The initial existence of the sliding mode is guaranteed by the proposed control law. The improvement of the proposed control scheme performances, such as chattering elimination and estimation of norm bounds of uncertainties, is then considered with the application of an adaptive fuzzy integral sliding mode control law. The validity and efficiency of the proposed approaches are investigated through a sixth order uncertain mechanical system.
LA - eng
KW - adaptive fuzzy control; integral sliding mode; LMI; mismatched uncertainties
UR - http://eudml.org/doc/208073
ER -

References

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  2. Boyd, S., Ghaoui, L.E., Feron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics, Philadelphia, PA. Zbl0816.93004
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  10. Mnasri, C. and Gasmi, M. (2007a). Decentralized sliding mode control for linear interconnected systems, Proceedings of the 4th International Multi-Conference on Systems Signals and Devices, SSD 2007, Hammamet, Tunisia. Zbl1283.93064
  11. Mnasri, C. and Gasmi, M. (2007b). Robust decentralized sliding mode control for large scale uncertain systems, Proceedings of the 26th Chinese Control Conference, CCC 2007, Hunan, China, pp. 76-81. 
  12. Mnasri, C. and Gasmi, M. (2008). Adaptive fuzzy sliding mode model-reference control for mimo uncertain systems, International Review of Automatic Control, IREACO 01(2): 143-152. 
  13. Shaocheng, Q. and Yongji, W. (2006). Robust control of uncertain time delay system: A novel sliding mode control design via LMI, Journal of Systems Engineering and Electronics 17(3): 624-628. Zbl1302.93086
  14. Utkin, V.I. (1992). Sliding Modes in Control and Optimization, Springer-Verlag, Berlin. Zbl0748.93044
  15. Utkin, V.I. and Shi, J. (1996). Integral sliding mode in systems operating under uncertainty conditions, Proceedings of the 35th Conference on Decision and Control, Kobe, Japan, pp. 4591-4596. 
  16. Wang, L.X. (1997). A Course in Fuzzy Systems and Control, Prentice Hall, Englewood Cliffs, NJ. Zbl0910.93002
  17. Xia, Y. and Jia, Y. (2003). Robust sliding mode control design of uncertain time-delay systems: An LMI approach, IEEE Transactions on Automatic Control 48(6): 624-628. 

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