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

Xin Meng; Cunchen Gao; Baoping Jiang; Hamid Reza Karimi

doi:10.3934/dcdss.2022027

Article Contents

2022, Volume 15, Issue 11: 3261-3274. Doi: 10.3934/dcdss.2022027

This issue Previous Article Bounded consensus of double-integrator stochastic multi-agent systems Next Article Pinning detectability of Boolean control networks with injection mode

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

1.
School of Mathematical Sciences, Ocean University of China, Qingdao, China
2.
School of Electronic and Information Engineering, Suzhou University of Science and Technology, Suzhou, China
3.
Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy

^* Corresponding author: Baoping Jiang and Hamid Reza Karimi
^* Corresponding author: Baoping Jiang and Hamid Reza Karimi

Received: July 31, 2021

Revised: November 30, 2021

Early access: February 2022

Published: September 2022

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Abstract

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.

Keywords:

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

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

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Figure 2. State trajectories of open-loop systems

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Figure 3. The curves of disturbance estimation

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Figure 4. State trajectories of closed-loop systems

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

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

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

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