  We investigate adaptive strategies to robustly and optimally control the
COVID-19 pandemic via social distancing measures based on the example of
Germany. Our goal is to minimize the number of fatalities over the course of
two years without inducing excessive social costs. We consider a tailored model
of the German COVID-19 outbreak with different parameter sets to design and
validate our approach. Our analysis reveals that an open-loop optimal control
policy can significantly decrease the number of fatalities when compared to
simpler policies under the assumption of exact model knowledge. In a more
realistic scenario with uncertain data and model mismatch, a feedback strategy
that updates the policy weekly using model predictive control (MPC) leads to a
reliable performance, even when applied to a validation model with deviant
parameters. On top of that, we propose a robust MPC-based feedback policy using
interval arithmetic that adapts the social distancing measures cautiously and
safely, thus leading to a minimum number of fatalities even if measurements are
inaccurate and the infection rates cannot be precisely specified by social
distancing. Our theoretical findings support various recent studies by showing
that 1) adaptive feedback strategies are required to reliably contain the
COVID-19 outbreak, 2) well-designed policies can significantly reduce the
number of fatalities compared to simpler ones while keeping the amount of
social distancing measures on the same level, and 3) imposing stronger social
distancing measures early on is more effective and cheaper in the long run than
opening up too soon and restoring stricter measures at a later time.
