  In this paper, we formulate a Nonlinear Model Predictive Control (NMPC) to
plan appropriate social distancing measures (and relaxations) in order to
mitigate the COVID-19 pandemic effects, considering the contagion development
in Brazil. The NMPC strategy is designed upon an adapted data-driven
Susceptible-Infected-Recovered-Deceased (SIRD) contagion model, which takes
into account the effects of social distancing. Furthermore, the adapted SIRD
model includes time-varying auto-regressive contagion parameters, which
dynamically converge according to the stage of the pandemic. This new model is
identified through a three-layered procedures, with analytical regressions,
Least-Squares optimization runs and auto-regressive model fits. The data-driven
model is validated and shown to adequately describe the contagion curves over
large forecast horizons. In this model, control input is defined as finitely
parametrized values for social distancing guidelines, which directly affect the
transmission and infection rates of the SARS-CoV-2 virus. The NMPC strategy
generates piece-wise constant quarantine guidelines which can be
relaxed/strengthen as each week passes. The implementation of the method is
pursued through a search mechanism, since the control is finitely parametrized
and, thus, there exist a finite number of possible control sequences.
Simulation essays are shown to illustrate the results obtained with the
proposed closed-loop NMPC strategy, which is able to mitigate the number of
infections and progressively loosen social distancing measures. With respect to
an "open-loop"/no control condition, the number of deaths still could be
reduced in up to 30 %. The forecast preview an infection peak to September 2nd,
2020, which could lead to over 1.5 million deaths if no coordinate health
policy is enacted. The framework serves as guidelines for possible public
health policies in Brazil.
