Abstract
Sliding mode control of uncertain T–S fuzzy systems is investigated, aiming to remove the restrict assumptions required in the existing results. We propose a novel dynamic sliding mode control (DSMC) scheme for T–S fuzzy models, aiming to eliminate the restrictive assumption that all subsystems share a common input matrix, which is required in most existing fuzzy SMC approaches. Sufficient conditions for the reachability of the sliding surface and asymptotic stability of the sliding motion are formulated in the form of linear matrix inequalities. Finally, simulation results illustrating the advantages and effectiveness of the proposed approaches are provided.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Utkin, V. I. (1977). Variable structure systems with sliding modes. IEEE Transactions on Automatic Control, AC–22(2), 212–222.
Hung, J. Y., Gao, W., & Hung, J. C. (1993). Variable structure control: A survey. IEEE Transactions on Industrial Electronics, 40(1), 2–22.
Gao, W., & Hung, J. C. (1993). Variable structure control of nonlinear systems: A new approach. IEEE Transactions on Industrial Electronics, 40(1), 45–55.
Young, K. D., Utkin, V. I., & Ozguner, U. (1999). A control engineer’s guide to sliding mode control. IEEE Transactions on Control Systems Technology, 7(3), 328–342.
Utkin, V. I. (1993). Sliding mode control design principles and applications to electric drives. IEEE Transactions on Industrial Electronics, 40(1), 23–26.
Punta, E., Bartolini, G., Pisano, A., & Usai, E. (2003). A survey of applications of second-order sliding mode control to mechanical systems. International Journal of Control, 76, 875–892.
Yu, X., Man, Z., & Wu, B. (1998). Design of fuzzy sliding-mode control systems. Fuzzy Sets and Systems, 95(3), 295–306.
Zhang, J., Shi, P., & Xia, Y. (2010). Robust adaptive sliding-mode control for fuzzy systems with mismatched uncertainties. IEEE Transactions on Fuzzy Systems, 18(4), 700–711.
Lin, C., Wang, Q., & Lee, T. H. (2005). Stabilization of uncertain fuzzy time-delay systems via variable structure control approach. IEEE Transactions on Fuzzy Systems, 13(6), 787–798.
Choi, H. H. (2010). Robust stabilization of uncertain fuzzy-time-delay systems using sliding-mode-control approach. IEEE Transactions on Fuzzy Systems, 18(5), 979–984.
Xi, Z., Feng, G., & Hesketh, T. (2011). Piecewise sliding-mode control for T-S fuzzy systems. IEEE Transactions on Fuzzy Systems, 19(4), 707–716.
Xi, Z., Feng, G., & Hwsketh, T. (2011). Piecewise integral sliding-mode control for T-S fuzzy systems. IEEE Transactions on Fuzzy Systems, 19(1), 65–74.
Ho, D. W. C., & Niu, Y. (2007). Robust fuzzy design for nonlinear uncertain stochastic systems via sliding-mode control. IEEE Transactions on Fuzzy Systems, 15(3), 350–358.
Wang, J., Rad, A. B., & Chan, P. T. (2001). Indirect adaptive fuzzy sliding mode control: Part I: Fuzzy switching. Fuzzy Sets and Systems, 122(1), 21–30.
Wang, J., Rad, A. B., & Chan, P. T. (2001). Indirect adaptive fuzzy sliding mode control: Part II: Parameter projection and supervisory control. Fuzzy Sets and Systems, 122(1), 31–43.
Tanaka, K., & Wang, H. O. (2001). Fuzzy control systems design and analysis: A LMI approach. New York: Wiley.
Choi, H. H. (2008). Robust stabilization of uncertain fuzzy systems using variable structure system approach. IEEE Transactions on Fuzzy Systems, 16(3), 715–724.
Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in systems and control theory. Philadelphia: SIAM.
Chen, M., & Feng, G. (2009). Delay-dependent \({\fancyscript {H}}_{\infty }\) filter design for discrete time fuzzy systems with time-varying delays. IEEE Transactions on Fuzzy Systems, 17(3), 604–616.
Lin, C., Wang, Q., Lee, T. H., & He, Y. (2008). Design of observer-based \({\fancyscript {H}}_{\infty }\) control for fuzzy time-delay systems. IEEE Transactions on Fuzzy Systems, 16(2), 534–543.
Huang, L., & Mao, X. (2010). SMC design for robust \({\fancyscript {H}}_{\infty }\) control of uncertain stochastic delay systems. Automatica, 46(2), 405–412.
Mao, X. (2007). Stochastic differential equations and applications (2nd ed.). Chichester: Horwood Publication.
Niu, Y., Ho, D. W. C., & Wang, X. (2008). Robust \({{\fancyscript {H}}_{\infty }}\) control for nonlinear stochastic systems: A sliding-mode approach. IEEE Transactions on Automatic Control, 53(7), 1695–1701.
Niu, Y., & Ho, D. W. C. (2006). Robust observer design for \(It\hat{o}\) stochastic time-delay systems via sliding mode control. Systems and Control Letters, 55(10), 781–793.
Gao, Q., Feng, G., Wang, Y., & Qiu, J. (2013). Universal fuzzy models and universal fuzzy controllers for stochastic non-affine nonlinear systems. IEEE Transactions on Fuzzy Systems, 21(2), 328–341.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer Science+Business Media Singapore
About this chapter
Cite this chapter
Gao, Q. (2017). Sliding Mode Control Based on T–S Fuzzy Models. In: Universal Fuzzy Controllers for Non-affine Nonlinear Systems. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-1974-6_4
Download citation
DOI: https://doi.org/10.1007/978-981-10-1974-6_4
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-1973-9
Online ISBN: 978-981-10-1974-6
eBook Packages: EngineeringEngineering (R0)