Controle realimentado de admissões nas diferentes etapas de um ciclo de vacinação via álgebra tropical

Abstract

This Master’s dissertation presents the development of a model for a vaccination center. The first goal is to provide a model that captures the main characteristics of the center dynamics, allowing a better undertanding of its behavior under critical conditions. A second goal is to use the model for designing a controller capable of restricting users admissions to the different stages of the center’s operation in order to meet the requirements of social distancing protocols issued by sanitary authorities due to Covid pandemic. At the same time, the controller is expecteded to minimize users’ waiting time while keeping the center’s vaccination rate as high as possible. The vaccination center is modelled as a Petri’s net. Specifically, it is modelled as a timed event graph. The tropical algebra toolbox is used to describe its behavior mathematically. Once the model is developed, it is used to design the controller. It is shown that the causalization of the control matrix is a critical step for the controller design. Two methods for causalization are discussed and a small theoretical contribution is given to one of them. The system is then simulated and it is shown that the results confirm the theoretical predictions, attesting the potencial benefit of utilizing the model developed here to improve vaccination center’s operation.