Abstract
In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.
Similar content being viewed by others
References
Ott, E., Grebogi, C., Yorke, J.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)
Yu, X., Chen, G., Xia, Y., Song, Y., Cao, Z.: An invariant-manifold-based method for chaos control. IEEE Trans. Circuits Syst. I, Fundam. Theor. Appl. 48, 930–937 (2001)
Liao, X., Yu, P.: Chaos control for the family of Rössler systems using feedback controllers. Chaos Solitons Fractals 29, 91–107 (2006)
Hugues-Salas, O., Banks, S.P.: Optimal control of chaos in nonlinear driven oscillators via linear time-varying approximations. Int. J. Bifurc. Chaos 18, 3355–3374 (2008)
Feki, M.: An adaptive feedback control of linearizable chaotic systems. Chaos Solitons Fractals 15, 883–890 (2003)
Hua, C., Guan, X.: Adaptive control for chaotic systems. Chaos Solitons Fractals 22, 55–60 (2004)
Feng, G., Chen, G.: Adaptive control of discrete-time chaotic systems: a fuzzy control approach. Chaos Solitons Fractals 23, 459–467 (2005)
Chen, B., Liu, X., Tong, S.: Adaptive fuzzy approach to control unified chaotic systems. Chaos Solitons Fractals 34, 1180–1187 (2007)
Chang, J.F., Hung, M.L., Yang, Y.S., Liao, T.L., Yan, J.J.: Controlling chaos of the family of Rössler systems using sliding mode control. Chaos Solitons Fractals 37, 609–622 (2008)
Khoo, S., Man, Z., Zhao, S.: Comments on “Adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties”. Automatica 44, 2995–2998 (2008)
Dadras, S., Momeni, H.R.: Control uncertain Genesio-Tesi chaotic system: adaptive sliding mode approach. Chaos Solitons Fractals 42, 3140–3146 (2009)
Hung, J.Y., Gao, W., Hung, J.C.: Variable structure control: a survey. IEEE Trans. Ind. Electron. 40, 2–22 (1993)
Edward, C., Spurgeon, S.K.: Sliding Mode Control: Theory and Applications. Taylor & Francis, London (1998)
Yu, X., Kaynak, O.: Sliding-mode control with soft computing: a survey. IEEE Trans. Ind. Electron. 56, 3275–3285 (2009)
Poursamad, A., Markazi, Amir H.D.: Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems. Chaos Solitons Fractals 42, 3100–3109 (2009)
Liang, Q., Mendel, J.M.: Interval type-2 fuzzy logic systems: theory and design. IEEE Trans. Fuzzy Syst. 8, 535–550 (2000)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning I. Inform. Sci. 8, 199–249 (1975)
Ying, H., Siler, W., Buckley, J.J.: Fuzzy control theory: a nonlinear case. Automatica 26, 513–520 (1990)
Park, C.W., Lee, C.H., Park, M.: Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty. Inform. Sci. 147, 245–266 (2002)
Slotine, J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, New Jersey (1991)
Wai, R.J., Lin, C.M., Hsu, C.F.: Adaptive fuzzy sliding-mode control for electrical servo drive. Fuzzy Sets Syst. 143, 295–310 (2004)
Poursamad, A., Davaie-Markazi, A.H.: Robust adaptive fuzzy control of unknown chaotic systems. Appl. Soft Comput. J. 9, 970–976 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hwang, Jh., Kwak, Hj. & Park, Gt. Adaptive interval type-2 fuzzy sliding mode control for unknown chaotic system. Nonlinear Dyn 63, 491–502 (2011). https://doi.org/10.1007/s11071-010-9817-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-010-9817-0