Sliding mode preview control for discrete SIR model based on modified Euler method

Chenqi Wang; Yuan Li; Yi Zhang

doi:10.3934/mfc.2024049

Article Contents

2025, Volume 8, Issue 6: 1036-1047. Doi: 10.3934/mfc.2024049

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Sliding mode preview control for discrete SIR model based on modified Euler method

School of Science, Shenyang University of Technology, China

^*Corresponding author: Yuan Li
^*Corresponding author: Yuan Li

Received: October 2024

Revised: November 2024

Early access: December 9, 2024

Published online: December 9, 2024

The first author is supported by [the Young Scientists Fund of the National Natural Science Foundation (NNSF) of China under Grant 62403423].

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Abstract

In this paper, for a class of SIR models with saturated incidence, the SIR model is discretized using the modified Euler method to form a form in which the coefficient matrix contains unknown parameters. The augmented error system method is constructed and the future information is simulated as a feed-forward and compensated into the SIR model, and the output regulation method of the linear discrete system is used to design the non-singular terminal sliding mode surface and the exponential convergence law, and the suitable performance index is given to obtain the optimal sliding mode preview controller. Finally, numerical simulation is utilized to verify the effectiveness of the theory and methodology of this paper.

Keywords:

Modified Euler method,
non-singular terminal sliding mode surface,
preview control,
optimal control,
saturated incidence.

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

Citation:

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Figure 1. Schematic diagram of optimal sliding mode preview control for SIR model

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Figure 2. Trend of SIR model without control

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Figure 3. Trend of SIR model after applying control

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Figure 4. Objective function

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Figure 5. Tracking error

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