This paper formulates a Model Predictive Control (MPC) policy to mitigate the COVID-19 contagion in Brazil, designed as optimal On-Off social isolation strategy. The proposed optimization algorithm is able to determine the time and duration of social distancing policies in the country. The achieved results are based on data from the period between March and May of 2020, regarding the cumulative number of infections and deaths due to the SARS-CoV-2 virus. This dataset is assumably largely sub-notified due to the absence of mass testing in Brazil. Thus, the MPC is based on a SIR model which is identified using an uncertainty-weighted Least-Squares criterion. Furthermore, this model includes an additional dynamic variable that mimics the response of the population to the social distancing policies determined by the government, which affect the COVID-19 transmission rate. The proposed control method is set within a mixed-logical formalism, since the decision variable is forcefully binary (existence or the absence of social distance policy). A dwell-time constraint is included to avoid too frequent shifts between these two inputs. The achieved simulation results illustrate how such optimal control method would operate in practice, pointing out that no social distancing should be relaxed before mid August 2020. If relaxations are necessary, they should not be performed before this date and should be in small periods, no longer than 25 days. This paradigm would proceed roughly until January/2021. The results also indicate a possible second peak of infections, which has a forecast to the beginning of October. This peak can be reduced if the periods of days with relaxed social isolation measures are shortened.

本文制定了模型预测控制 (MPC) 政策，以减轻巴西的 COVID-19 传染，该政策被设计为最佳的开关社交隔离策略。所提出的优化算法能够确定该国社会疏远政策的时间和持续时间。所取得的结果基于 2020 年 3 月至 5 月期间有关 SARS-CoV-2 病毒累计感染和死亡人数的数据。由于巴西缺乏大规模测试，该数据集可能很大程度上是次通知的。因此，MPC 基于 SIR 模型，该模型使用不确定性加权最小二乘准则进行识别。此外，该模型还包括一个额外的动态变量，该变量模仿人口对政府确定的社会疏远政策的反应，这会影响 COVID-19 的传播率。所提出的控制方法是在混合逻辑形式主义中设置的，因为决策变量是强制二元的（存在或不存在社交距离政策）。包含停留时间限制以避免这两个输入之间过于频繁的转换。所取得的模拟结果说明了这种最优控制方法在实践中的运作方式，指出在2020年8月中旬之前不应放松社交距离。如果需要放松，则不应在此日期之前放松，并且应该是小周期、不放松。超过25天。这种模式将大致持续到 2021 年 1 月。结果还表明可能出现第二次感染高峰，预计到十月初。如果缩短放松社交隔离措施的时间，这一高峰就可以减少。