Advertisement

Universal Fuzzy Integral Sliding-Mode Controllers for Stochastic Non-affine Nonlinear Systems

  • Qing GaoEmail author
Chapter
  • 469 Downloads
Part of the Springer Theses book series (Springer Theses)

Abstract

In this paper, the universal integral sliding-mode controller problem for general stochastic nonlinear systems modeled by \(It\hat{o}\) type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T–S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.

References

  1. 1.
    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.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Niu, Y., Ho, D. W. C. & Lam, J. (2005). “Robust integral sliding mode control for uncertain stochastic systems with time-varying delay”. Automatica, 41(5), 873–880.Google Scholar
  3. 3.
    Niu, Y., Ho, D. W. C., & Wang, X. (2007). “Sliding mode control for \(It\hat{o}\) stochastic systems with Markovian switching”. Automatica, 43(10), 1784–1790.Google Scholar
  4. 4.
    Niu, Y., & Ho, D. W. C. (2006). “Robust observer design for \(It\hat{o}\) stochastic time-delay systems via sliding mode control”. Systems & Control Letters, 55(10), 781–793.Google Scholar
  5. 5.
    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.CrossRefGoogle Scholar
  6. 6.
    Mao, X. (2007). Stochastic Differential Equations and Applications (2nd ed.). Chichester, UK: Horwood Publication.zbMATHGoogle Scholar
  7. 7.
    Tsinias, J., & Spiliotis, J. (1999). "A converse Lyapunov theorem for robust exponential stochastic stability," Lecture Notes in Control and Information Sciences, Workshop of the Nonlinear Control. Ghent. Springer: Berlin, 246, 355–374.MathSciNetzbMATHGoogle Scholar
  8. 8.
    Tsinias, J. (1998). Stochast input-to-state stability and applications to global feedback stabilization. International Journal of Control, 71(5), 907–930.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    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.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.City University of Hong KongHong KongChina

Personalised recommendations