A learning-based model predictive control framework with a state observer for epidemic mitigation

Resumen

Many applications have shown the use and success of classical compartment models in estimating the states and evolution of disease spreads. Similarly, the study of Optimal Control Theory has shown positive results in those scenarios but, sometimes, lack computational and theoretical tractability, especially in the cases of long-term problems or uncertain scenarios. In that context, Model Predictive Control (MPC) has become apparent, as it provides a more tractable version of a (Stochastic) Optimal Control Problem by approximating the solution through a simplified version of the control problem over a shorter horizon. Nevertheless, the current state or uncertainty can affect the local optimal solution, which provides niche to the introduction of learning methods in the process. From this perspective, we propose a Learning-Based Model Predictive Control strategy for a susceptible-infected-recovered-quarantine (SIRQ) model for an uncertain scenario, where one has only reliable measures of the population in (Q)uarantine. For this work, a testing for isolation control strategy is proposed, also considered reliably measurable. We show how this kind of approach could be a reliable option for epidemic disease mitigation. Future works include the discussion of a more complete set of compartments, for vaccine effectiveness estimation, and robust control under uncertain vaccination availability.