Probabilistic robust anti-disturbance control of uncertain systems

Peng Cheng; Feng Pan; Yanyan Yin; Song Wang

doi:10.3934/jimo.2020076

Article Contents

2021, Volume 17, Issue 5: 2441-2450. Doi: 10.3934/jimo.2020076

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Probabilistic robust anti-disturbance control of uncertain systems

1.
Key laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, China
2.
School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, Western Australia, 6102, Australia
3.
School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, GPO Box U1987, Perth, WA6845, Australia
4.
Shenzhen Audencia Business School, WeBank Institute of Fintech, Guangdong Laboratory of Artificial Intelligence and Digital Economics (SZ), Shenzhen University, Shenzhen, 518060, China

^* Corresponding author: Feng Pan
^* Corresponding author: Feng Pan

Received: May 2019

Revised: October 2019

Early access: April 2020

Published: September 2021

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Abstract

We propose a novel method for constructing probabilistic robust disturbance rejection control for uncertain systems in which a scenario optimization method is used to deal with the nonlinear and unbounded uncertainties. For anti-disturbance, a reduced order disturbance observer is considered and a state-feedback controller is designed. Sufficient conditions are presented to ensure that the resulting closed-loop system is stable and a prescribed $ H_{\infty} $ performance index is satisfied. A numerical example is presented to illustrate the effectiveness of the techniques proposed and analyzed.

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Mathematics Subject Classification: Primary: 93C55, 93D09; Secondary: 93B05.

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Figure 1. State trajectory of a-posteriori Monte-Carlo analysis

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Figure 2. Estimation of disturbance

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Figure 3. Trajectory of controlled output

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