Real-Time Optimization of Social Distancing to Mitigate COVID-19 Pandemic Using Quantized Extremum Seeking

The application of extremum seeking control is investigated to mitigate the spread of the COVID-19 pandemic, maximizing social distancing while limiting the number of infections. The procedure does not rely on the accurate knowledge of an epidemiological model and takes realistic constraints into account, such as hospital capacities, the observation horizon of the pandemic evolution and the quantized government sanitary policy decisions. Based on the bifurcation analysis of a SEIARD compartmental model providing two possible types of equilibria, numerical simulation reveals the transient behaviour of the extremum of the constrained cost function, which, if rapidly caught by the algorithm, slowly drifts to the steady-state optimum. Specific features are easily incorporated in the real-time optimization procedure, such as quantized sanitary condition levels and long actuation (decision) periods (usually several weeks), requiring processing of the discrete control signal saturation and quantization. The performance of the proposed method is numerically assessed, considering the convergence rate and accuracy (quantization bias).