Feedback stabilization and observer design for sterile insect technique models

Kala Agbo Bidi; Kala Agbo Bidi

doi:10.3934/mbe.2024274

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 6: 6263-6288. doi: 10.3934/mbe.2024274

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Feedback stabilization and observer design for sterile insect technique models

Kala Agbo Bidi ^,

Sorbonne Université, CNRS, Université Paris-Cité, Laboratoire Jacques-Louis Lions, LJLL, INRIA équipe CAGE, Paris F-75005, France

Received: 30 January 2024 Revised: 10 May 2024 Accepted: 03 June 2024 Published: 13 June 2024

This paper focuses on the feedback global stabilization and observer construction for a sterile insect technique model. The sterile insect technique (SIT) is one of the most ecological methods for controlling insect pests responsible for worldwide crop destruction and disease transmission. In this work, we construct a feedback law that globally asymptotically stabilizes an SIT model at extinction equilibrium. Since the application of this type of control requires the measurement of different states of the target insect population, and, in practice, some states are more difficult or more expensive to measure than others, it is important to know how to construct a state estimator, which from a few well-chosen measured states, estimates the other ones, as the one we build in the second part of our work. In the last part of our work, we show that we can apply the feedback control with estimated states to stabilize the full system.
- sterile insect technique,
- pest control,
- feedback control design,
- observer design,
- Lyapunov stability,
- mosquito population control,
- vector-borne disease
Citation: Kala Agbo Bidi. Feedback stabilization and observer design for sterile insect technique models[J]. Mathematical Biosciences and Engineering, 2024, 21(6): 6263-6288. doi: 10.3934/mbe.2024274

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Abstract

This paper focuses on the feedback global stabilization and observer construction for a sterile insect technique model. The sterile insect technique (SIT) is one of the most ecological methods for controlling insect pests responsible for worldwide crop destruction and disease transmission. In this work, we construct a feedback law that globally asymptotically stabilizes an SIT model at extinction equilibrium. Since the application of this type of control requires the measurement of different states of the target insect population, and, in practice, some states are more difficult or more expensive to measure than others, it is important to know how to construct a state estimator, which from a few well-chosen measured states, estimates the other ones, as the one we build in the second part of our work. In the last part of our work, we show that we can apply the feedback control with estimated states to stabilize the full system.

References

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