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 eectively lead to a good trade-o 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-o is a highly uncertain quantity that cannot be xed 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 specic 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 ne-tuning the
control parameters. Finally, we validate the results through numerical simulations tailored on the COVID-19 outbreak.
