Observer-based output feedback for an age-structured SIRD model

Abstract

An age-structured Susceptible-Infected-Recovered-Deceased (SIRD) epidemic model is considered. The aim of this paper is to design an observer-based output feedback control law, representing an immunization process, typically vaccination, intended to decrease the peak of infected individuals in the population. At first, well-posedness and stability of the system in open-loop are investigated. Then, to obtain the observer-based output feedback law, a state feedback law is designed by using a normal form. Conditions to ensure stability are established. However, due to physical constraints, this law needs to be adapted. Therefore, a constrained state-feedback law is implemented. This law is designed to fulfill the physical constraints while having good properties (Lipschitz for instance), needed for the last part of the article. Finally, an observer-based output feedback law is obtained using high-gain observer. At each step of the design, convergence properties are obtained. Finally, numerical simulations are performed.

Figures (10)

• Figure 1: Representation of the construction of the constrained feedback-law, $\theta_{sat_k}(x)$
• Figure 2: Representation of the control law $\theta_{sat_k}(t)$
• Figure 3: Illustration of the finite number of jumps for the saturated control law, $\theta_{sat_k}(t)$
• Figure 4: Dynamics of the proportion of infected individuals without control
• Figure 5: Dynamics of the proportion of susceptible individuals without control