Convex output feedback model predictive control for mitigation of COVID-19 pandemic

In this paper, a model predictive control approach is proposed for epidemic mitigation. The disease spreading dynamics is described by an 8-compartment smooth nonlinear model of the COVID-19 pandemic in Hungary known from the literature, where the manipulable control input is the stringency of the introduced non-pharmaceutical measures. It is assumed that only the number of hospitalized people is measured on-line, and the other state variables are computed using a state observer which is based on the dynamic inversion of a linear sub-system of the model. The objective function contains a measure of the direct harmful consequences of the restrictions, and the constraints refer to input bounds and to the capacity of the healthcare system. By exploiting the special properties of the model, the nonlinear optimization problem required by the control design is reformulated to convex tasks, allowing a computationally efficient solution. Two approaches are proposed: the first finds a suboptimal solution by geometric programming, while the second one further simplifies the problem and transforms it to a linear programming task. Simulations show that both suboptimal solutions fulfill the design specifications even in the presence of parameter uncertainties.