Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent

Hoda Moodi; Mohammad Farrokhi

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 4, page 711-723
  • ISSN: 1641-876X

Abstract

top
This paper is concerned with observer design for nonlinear systems that are modeled by T-S fuzzy systems containing parametric and nonparametric uncertainties. Unlike most Sugeno models, the proposed method contains nonlinear functions in the consequent part of the fuzzy IF-THEN rules. This will allow modeling a wider class of systems with smaller modeling errors. The consequent part of each rule contains a linear part plus a nonlinear term, which has an incremental quadratic constraint. This constraint relaxes the conservativeness introduced by other regular constraints for nonlinearities such as the Lipschitz conditions. To further reduce the conservativeness, a nonlinear injection term is added to the observer dynamics. Simulation examples show the effectiveness of the proposed method compared with the existing techniques reported in well-established journals.

How to cite

top

Hoda Moodi, and Mohammad Farrokhi. "Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent." International Journal of Applied Mathematics and Computer Science 23.4 (2013): 711-723. <http://eudml.org/doc/262484>.

@article{HodaMoodi2013,
abstract = {This paper is concerned with observer design for nonlinear systems that are modeled by T-S fuzzy systems containing parametric and nonparametric uncertainties. Unlike most Sugeno models, the proposed method contains nonlinear functions in the consequent part of the fuzzy IF-THEN rules. This will allow modeling a wider class of systems with smaller modeling errors. The consequent part of each rule contains a linear part plus a nonlinear term, which has an incremental quadratic constraint. This constraint relaxes the conservativeness introduced by other regular constraints for nonlinearities such as the Lipschitz conditions. To further reduce the conservativeness, a nonlinear injection term is added to the observer dynamics. Simulation examples show the effectiveness of the proposed method compared with the existing techniques reported in well-established journals.},
author = {Hoda Moodi, Mohammad Farrokhi},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {nonlinear Sugeno model; incremental quadratic constraint; robust observer},
language = {eng},
number = {4},
pages = {711-723},
title = {Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent},
url = {http://eudml.org/doc/262484},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Hoda Moodi
AU - Mohammad Farrokhi
TI - Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 4
SP - 711
EP - 723
AB - This paper is concerned with observer design for nonlinear systems that are modeled by T-S fuzzy systems containing parametric and nonparametric uncertainties. Unlike most Sugeno models, the proposed method contains nonlinear functions in the consequent part of the fuzzy IF-THEN rules. This will allow modeling a wider class of systems with smaller modeling errors. The consequent part of each rule contains a linear part plus a nonlinear term, which has an incremental quadratic constraint. This constraint relaxes the conservativeness introduced by other regular constraints for nonlinearities such as the Lipschitz conditions. To further reduce the conservativeness, a nonlinear injection term is added to the observer dynamics. Simulation examples show the effectiveness of the proposed method compared with the existing techniques reported in well-established journals.
LA - eng
KW - nonlinear Sugeno model; incremental quadratic constraint; robust observer
UR - http://eudml.org/doc/262484
ER -

References

top
  1. Abdelmalek, I., Golea, N. and Hadjili, M.L. (2007). A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models, International Journal of Applied Mathematics and Computer Science 17(1): 39-51, DOI: 10.2478/v10006-007-0005-4. Zbl1133.93032
  2. Açikmese, A.B. and Corless, M. (2011). Observers for systems with nonlinearities satisfying incremental quadratic constraints, Automatica 47(7): 1339-1348. Zbl1219.93016
  3. Asemani, M.H. and Majd, V.J. (2013). A robust observer-based controller design for uncertain T-S fuzzy systems with unknown premise variables via LMI, Fuzzy Sets and Systems 212: 21-40. Zbl1285.93051
  4. Bernal, M. and Hušek, P. (2005). Non-quadratic performance design for Takagi-Sugeno fuzzy systems, International Journal of Applied Mathematics and Computer Science 15(3): 383-391. Zbl1169.93355
  5. Boyd, S., Ghaoui, L.E., Feron, E. and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, Philadelphia, PA. Zbl0816.93004
  6. Chadli, M. and Guerra, T.M. (2012). LMI solution for robust static output feedback control of discrete Takagi-Sugeno fuzzy models, IEEE Transactions on Fuzzy Systems 20(6): 1160-1165. 
  7. Dong, J., Wang, Y. and Yang, G.H. (2011). H ∞ and mixed H₂/ H ∞ control of discrete-time T-S fuzzy systems with local nonlinear models,, Fuzzy Sets and Systems 164(1): 1-24. 
  8. Dong, J., Wang, Y. and Yang, G.H. (2010). Output feedback fuzzy controller design with local nonlinear feedback laws for discrete-time nonlinear systems, IEEE Transactions on Systems, Man and Cybernetics, B: Cybernetics 40(6): 1447-1459. 
  9. Faria, F.A., Silva, G.N. and Oliveira, V.A. (2012). Reducing the conservatism of LMI-based stabilisation conditions for T-S fuzzy systems using fuzzy Lyapunov functions, International Journal of Systems Science 44(10): 1956-1969, DOI: 10.1080/00207721.2012.670307. Zbl1307.93218
  10. Guerra, T.M. and Bernal, M. (2012). Strategies to exploit non-quadratic local stability analysis, International Journal of Fuzzy Systems 14(3): 372-379. 
  11. Guerra, T.M., Bernal, M., Guelton, K. and Labiod, S. (2012). Non-quadratic local stabilization for continuous-time Takagi-Sugeno models, Fuzzy Sets and Systems 201(16): 40-54. Zbl1251.93070
  12. Guerra, T.M., Kruszewski, A. and Lauber, J. (2009). Discrete Tagaki-Sugeno models for control: Where are we?, Annual Reviews in Control 33(1): 37-47. 
  13. Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2012). New fault tolerant control strategies for nonlinear Takagi-Sugeno systems, International Journal of Applied Mathematics and Computer Science 22(1): 197-210, DOI: 10.2478/v10006-012-0015-8. Zbl1273.93102
  14. Karagiannis, D., Jiang, Z., Ortega, R. and Astolfi, A. (2005). Output-feedback stabilization of a class of uncertain non-minimum phase nonlinear systems, Automatica 41(9): 1609-1615. Zbl1086.93021
  15. Löfberg, J. (2004). Yalmip: A toolbox for modeling and optimization in MATLAB, IEEE International Symposium on Computer Aided Control Systems Design, Taipei, Taiwan, pp. 284-289. 
  16. Lee, C. (2004). Stabilization of nonlinear non-minimum phase system: Adaptive parallel approach using recurrent fuzzy neural network, IEEE Transactions on Systems, Man and Cybernetics, Part B 34(2): 1075-1088. 
  17. Manai, Y. and Benrejeb, M. (2011). New condition of stabilization for continuous Takagi-Sugeno fuzzy system based on fuzzy Lyapunov function, International Journal of Control and Automation 4(3): 61-64. Zbl1264.93131
  18. Mozelli, L.A., Palhares, R.M. and Avellar, G.S.C. (2009). A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems, Information Sciences 179(8): 1149-1162. Zbl1156.93355
  19. Rajesh, R. and Kaimal, M.R. (2007). T-S fuzzy model with nonlinear consequence and PDC controller for a class of nonlinear control systems, Applied Soft Computing 7(3): 772-782. 
  20. Rhee, B.J. and Won, S. (2006). A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design, Fuzzy Sets and Systems 157(9): 1211-1228. Zbl1090.93025
  21. Sala, A. (2009). On the conservativeness of fuzzy and fuzzy-polynomial control of nonlinear systems, Annual Reviews in Control 33(1): 48-58. 
  22. Sala, A. and Arino, C. (2009). Polynomial fuzzy models for nonlinear control, a Taylor series approach, IEEE Transactions on Fuzzy Systems 17(6): 1284-1295. 
  23. Tanaka, K. and Wang, H.O. (2001). Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley and Sons, Inc., New York, NY. 
  24. Tseng, C.S., Chen, B.S. and Li, Y.F. (2009). Robust fuzzy observer-based fuzzy control design for nonlinear systems with persistent bounded disturbances: A novel decoupled approach, Fuzzy Sets and Systems 160(19): 2824-2843. Zbl1176.93050
  25. Tuan, H.D., Apkarian, P., Narikiyo, T. and Yamamoto, Y. (2001). Parameterized linear matrix inequality techniques in fuzzy control system design, IEEE Transactions on Fuzzy Systems 9(2): 324-332. 
  26. Xu, D., Jiang, B. and Shi, P. (2012). Nonlinear actuator fault estimation observer: An inverse system approach via a T-S fuzzy model, International Journal of Applied Mathematics and Computer Science 22(1): 183-196, DOI: 10.2478/v10006-012-0014-9. Zbl1273.93105
  27. Yoneyama, J. (2009). H ∞ filtering for fuzzy systems with immeasurable premise variables: An uncertain system approach, Fuzzy Sets and Systems 160(12): 1738-1748. Zbl1175.93137

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.