Fast transient optimization of social distancing during Covid-19 pandemics using extremum seeking

In this work, the application of a model-free extremum seeking strategy is investigated to achieve the hypothetical control of the covid-19 pandemics by acting on social distancing. The advantage of this procedure is that it does not rely on the accurate knowledge of an epidemiological model and takes realistic constraints into account, such as hospital capacities. The simulation study reveals that the convergence has two time scales, with a fast catch of the transient optimum of the measurable cost function, followed by a slow tracking of this optimum following the original SIR dynamics. Several issues are discussed such as quantization of the sanitary measures.