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

• Autorzy: Hoda Moodi , Mohammad Farrokhi
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

nonlinear Sugeno model; incremental quadratic constraint; robust observer

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2013
• Tom: 23
• Numer: 4
• Strony: 711-723

Daty

wydano

2013

otrzymano

2012-11-23

poprawiono

2013-04-16

poprawiono

2013-08-18

Twórcy

autor

Hoda Moodi

• Department of Electrical Engineering, Iran University of Science and Technology, Narmak, Farjam St., Tehran 16846, Iran

autor

Mohammad Farrokhi

• Department of Electrical Engineering, Iran University of Science and Technology, Narmak, Farjam St., Tehran 16846, Iran

Bibliografia

• 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.
• Açikmese, A.B. and Corless, M. (2011). Observers for systems with nonlinearities satisfying incremental quadratic constraints, Automatica 47(7): 1339-1348.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• Guerra, T.M. and Bernal, M. (2012). Strategies to exploit non-quadratic local stability analysis, International Journal of Fuzzy Systems 14(3): 372-379.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• Sala, A. (2009). On the conservativeness of fuzzy and fuzzy-polynomial control of nonlinear systems, Annual Reviews in Control 33(1): 48-58.
• 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.
• 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.
• 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.
• 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.
• 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.
• Yoneyama, J. (2009). $H_∞$ filtering for fuzzy systems with immeasurable premise variables: An uncertain system approach, Fuzzy Sets and Systems 160(12): 1738-1748.

Identyfikatory

DOI

10.2478/amcs-2013-0053