Hysteresis-based supervisory control with application to non-pharmaceutical containment of COVID-19.

The recent COVID-19 outbreak has motivated an extensive development of non-pharmaceutical intervention policies for epidemics containment. While a total lockdown is a viable solution, interesting policies are those allowing some degree of normal functioning of the society, as this allows a continued, albeit reduced, economic activity and lessens the many societal problems associated with a prolonged lockdown. Recent studies have provided evidence that fast periodic alternation of lockdown and normal-functioning days may effectively lead to a good trade-off between outbreak abatement and economic activity. Nevertheless, the correct number of normal days to allocate within each period in such a way to guarantee the desired trade-off is a highly uncertain quantity that cannot be fixed a priori and that must rather be adapted online from measured data. This adaptation task, in turn, is still a largely open problem, and it is the subject of this work. In particular, we study a class of solutions based on hysteresis logic. First, in a rather general setting, we provide general convergence and performance guarantees on the evolution of the decision variable. Then, in a more specific context relevant for epidemic control, we derive a set of results characterizing robustness with respect to uncertainty and giving insight about how a priori knowledge about the controlled process may be used for fine-tuning the control parameters. Finally, we validate the results through numerical simulations tailored on the COVID-19 outbreak.

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© 2021 The Author(s).

Déclaration de conflit d'intérêts

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.