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Observer-based SMC for stochastic systems with disturbance driven by fractional Brownian motion

  • * Corresponding author: Baoping Jiang and Hamid Reza Karimi

    * Corresponding author: Baoping Jiang and Hamid Reza Karimi 
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  • This paper investigates the problem of disturbance-observer-based sliding mode control for stabilization of stochastic systems driven by fractional Brownian motion (fBm). By proposing a novel disturbance observer, an integral-type sliding surface is put forward with the estimated disturbance error confined within a certain value. Meanwhile, by virtue of fractional infinitesimal operator and linear matrix inequality, a sufficient criterion is derived to guarantee the asymptotic stability of obtained sliding mode dynamics. Further, an observer-based sliding mode controller is designed to ensure finite-time reachability of state trajectories onto the predefined sliding surface. Lastly, an illustrative example is utilized to verify the reliability and applicability of the proposed control strategy.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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  • Figure 1.  A sample path of fBm with $ H = 0.6 $

    Figure 2.  State trajectories of open-loop systems

    Figure 3.  The curves of disturbance estimation

    Figure 4.  State trajectories of closed-loop systems

    Figure 5.  The curves of sliding mode surface function and control signal

    Figure 6.  State trajectories $ x_{1}(t) $ with $ \tau = 0.2,0.4,\cdot\cdot\cdot,1.0 $, respectively

    Figure 7.  State trajectories $ x_{2}(t) $ with $ \tau = 0.2,0.4,\cdot\cdot\cdot,1.0 $, respectively

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