PhD Comprehensive Seminar | Hassaan Qazi, Applications of Control Methods to Life Sciences

MC 6460 and MS Teams (please email amgrad@uwaterloo.ca for the meeting link)

Candidate

Hassaan Qazi | Applied Mathematics, University of Waterloo

Title

Applications of Control Methods to Life Sciences

Abstract

In our first project, we would like to design an optimal control law to release sterile mosquitoes that can mitigate the mosquito-borne diseases. Diseases that are caused by mosquito bites are a menace to humans worldwide as they cause lethal infections such as Dengue and Malaria. Since no vaccines are available, therefore it is imperative to control the population of mosquitoes. One of the strategies revolving around mosquito population reduction is a heavy use of insecticides. This method can have harmful impacts on the environment and may make mosquitoes resistant to these chemicals with time. The other strategy is to release genetically modified male mosquitoes in the wild so that they can mate with their female counterparts and make them infertile, which can significantly control the population growth. One challenging task is to find a neat trade-off between the number of sterile mosquitoes released and the cost attached to it. Impulsive control strategy seems to move in that direction where we develop a cost functional that takes both cost and the effectiveness of the release of sterile mosquitoes into account. In this study, we would like to extend the work presented by (Huang et. al., 2021) by imposing real-life constraints on the overall framework.

In the second project, a swarm of Unmanned Aerial Vehicles (UAVs) will be used for environment monitoring with applications in agriculture. This will be achieved by transporting the distribution of the multi-agent system towards the desired density distribution. The multi-agent system will be equipped with different sensors to take the required measurements over a field of interest at varying positions and times. The control strategy will be comprised of both centralized and decentralized hierarchies. The centralized controller is used to match the swarm distribution with the target distribution whereas decentralized controller will develop a low-level control law for each individual agent. There has been a growing interest in the study of mean-field feedback control that can make the swarm density converge to the desired distribution but optimal control strategies for the case when the agents’ states include stochastic behaviour has been limited. We would like to design optimal feedback control along with optimality conditions while incorporating energy and other constraints.