Article Contents
Article Contents

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

• * Corresponding author: Baoping Jiang and Hamid Reza Karimi
• 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.

 Citation:

• 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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