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Original Articles

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

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Pages 312-323 | Received 02 Dec 2016, Accepted 12 Nov 2017, Published online: 07 Dec 2017

References

  • Arnold, L. (1974). Stochastic differential equations: Theory and applications. New York, NY: John Wiley & Sons.
  • Bartolini, G., Ferrara, A., Giacomini, L., & Usai, A. (2000). Properties of a combined adaptive/second-order sliding mode control algorithm for some classes of uncertain nonlinear systems. IEEE Transactions on Automatic Control, 45, 1334–1341.
  • Deng, H., & Krstic, M. (1999). Output-feedback stochastic nonlinear stabilization. IEEE Transactions on Automatic Control, 44, 328–333.
  • Florchinger, P. (1995). Lyapunov-like techniques for stochastic stability. SIAM Journal on Control and Optimization, 33, 1151–1169.
  • Khalil, H. K. (2002). Nonlinear systems (3rd ed.). Upper Saddle River, NJ: Prentice-Hall.
  • Khasminskii, R. (2012). Stochastic stability of differential equations (2nd ed.), Berlin, Heidelberg: Springer.
  • Kuiava, R., Ramos, R. A., Pota, H. R., & Alberto, L. F. C. (2013). Practical stability of switched systems without a common equilibria and governed by a time-dependent switching signal. European Journal of Control, 19, 206–213.
  • Lakshmikantham, V., Leela, S., & Martynyuk, A. A. (1990). Practical stability of non-linear systems. Singapore: World Scientific.
  • Lakshmikantham, V., & Zhang, Y. (2001). Strict practical stability of delay differential equation. Applied Mathematics and Computation, 122, 341–351.
  • La Salle, J., & Lefschetz, S. (1961). Stability by Liapunov's direct method with applications. New York, NY: Academic Press.
  • Levant, A. (1993). Sliding order and sliding accuracy in sliding mode control. International Journal of Control, 58, 1246–1263.
  • Levant, A. (1998). Robust exact differentiation via sliding mode technique. Automatica, 34, 379–384.
  • Levant, A. (2003). Higher order sliding modes, differentiation and output-feedback control. International Journal of Control, 76, 924–941.
  • Niu, Y., Daniel, W. C. Ho., & Wang, X. (2008). Robust H∞ control for nonlinear stochastic systems: A sliding-mode approach. IEEE Transactions on Automatic Control, 53, 1695–1701.
  • Pan, Z., & Basar, T. (1999). Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost. SIAM Journal on Control and Optimization, 33, 957–995.
  • Qiu, J., Gao, H., & Ding, S. X. (2016). Recent advances on fuzzy-model-based nonlinear networked control systems: A survey. IEEE Transactions on Industrial Electronics, 63, 1207–1217.
  • Rao, C. R. (1973). Linear statistical inference and its applications (2nd ed.). New York, NY, USA: John Wiley & Sons.
  • Shtessel, Y. B., Edwards, C., Fridman, L., & Levant, A. (2014). Sliding mode control and observation. Berlin, Heidelberg: Springer.
  • Shtessel, Y. B., & Shkolnikov, I. A. (2003). Integrated guidance and control of advanced interceptors using second order sliding modes. In 42nd IEEE conference on decision and control. Advance online publication. (pp. 4587–4592), Piscataway, NJ, USA: IEEE.
  • Shtessel, Y. B., Shkolnikov, I. A., & Levant, A. (2007). Smooth second-order sliding modes: Missile guidance application. Automatica, 43, 1470–1476.
  • Slotine, J. E., & Li, W. (1991). Applied non-linear control. Englewood Cliffs, NJ: Prentice-Hall.
  • Song, X., Li, S., & Li, A. (2008). Practical stability of nonlinear differential equation with initial time difference. Applied Mathematics and Computation, 203, 157–162.
  • Utkin, V. I. (1992). Sliding modes in control optimization. Berlin, Heidelberg: Springer.
  • Utkin, V. I., & Shi, J. (1996). Integral sliding mode in systems operating under uncertainty conditions. In Proceedings of the 35th IEEE conference on decision and control (pp. 4591–4596). Piscataway, NJ, USA: IEEE.
  • Wang, T., Gao, H., & Qiu, J. (2016). A combined fault-tolerant and predictive control for network-based industrial processes. IEEE Transactions on Industrial Electronics, 63, 2529–2536.
  • Wang, T., Qiu, J., & Gao, H. (2016). Adaptive neural control of stochastic nonlinear time-delay systems with multiple constraints. IEEE Transactions on System, Man, and Cybernetics: System, 47, 1875–1883.
  • Wang, T., Qiu, J., Yin, S., Gao, H., Fan, J., & Chai, T. (2016). Performance-based adaptive fuzzy tracking control for networked industrial processes. IEEE Transactions on Cybernetics, 46, 1760–1770.
  • Wu, L., Zheng, W., & Gao, H. (2013). Dissipativity-based sliding mode control of switched stochastic systems. IEEE Transactions on Automatic Control, 58, 785–791.
  • Xu, X., Zhai, G., & He, S. (2007, July). Stabilizability and practical stabilizability of continuous-time switched systems: A unified view. In Proceedings of 2007 American control conference. Advance online publication. pp. 663–668, Evanston, ILL, USA: American Automatic Control Council.

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