Observer-based sliding mode controller design for singular bio-economic system with stochastic disturbance

Yi Zhang; Yuanpeng Zhao; Na Li; Yingying Wang; Yi Zhang; Yuanpeng Zhao; Na Li; Yingying Wang

doi:10.3934/math.2024072

AIMS Mathematics

2024, Volume 9, Issue 1: 1472-1493. doi: 10.3934/math.2024072

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Observer-based sliding mode controller design for singular bio-economic system with stochastic disturbance

School of Science, Shenyang University of Technology, Shenyang 110870, China

Received: 06 October 2023 Revised: 06 November 2023 Accepted: 20 November 2023 Published: 11 December 2023
MSC : 93C90, 93C05, 93D15, 93B52

In this paper, we investigate the problems of sliding mode observer design and observer-based integral sliding mode control for a class of singular bio-economic systems with stochastic disturbance. Initially, we establish a bio-economic system with the alien invasive species and stochastic disturbance. Then, a new integral sliding surface is constructed based on the multiplication of sliding variables and negative definite matrix for the error system. The advantage of this method is that it not only stabilizes the sliding variables, but also eliminates the restrictive assumptions often used in sliding mode control of the singular bio-economic systems with stochastic disturbance. Finally, an augmented system is constructed and the linear matrix inequality technique is used to determine the admissibility of the mean square exponent. Furthermore, an observer-based sliding mode controller is designed so that the reachability conditions can be guaranteed. The validity of the results is verified by a numerical simulation.
- sliding mode control,
- singular bio-economic systems,
- stochastic disturbance
Citation: Yi Zhang, Yuanpeng Zhao, Na Li, Yingying Wang. Observer-based sliding mode controller design for singular bio-economic system with stochastic disturbance[J]. AIMS Mathematics, 2024, 9(1): 1472-1493. doi: 10.3934/math.2024072

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Abstract

In this paper, we investigate the problems of sliding mode observer design and observer-based integral sliding mode control for a class of singular bio-economic systems with stochastic disturbance. Initially, we establish a bio-economic system with the alien invasive species and stochastic disturbance. Then, a new integral sliding surface is constructed based on the multiplication of sliding variables and negative definite matrix for the error system. The advantage of this method is that it not only stabilizes the sliding variables, but also eliminates the restrictive assumptions often used in sliding mode control of the singular bio-economic systems with stochastic disturbance. Finally, an augmented system is constructed and the linear matrix inequality technique is used to determine the admissibility of the mean square exponent. Furthermore, an observer-based sliding mode controller is designed so that the reachability conditions can be guaranteed. The validity of the results is verified by a numerical simulation.

References

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