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.

Motivated by the fact that many nonlinear plants can be represented through Linear Parameter Varying (LPV) embedding, and being this framework very popular for control design, this paper investigates the available Model Predictive Control (MPC) policies that can be applied for such systems. This paper reviews the available works considering LPV MPC design, ranging from the sub-optimal, simplified, yet Quadratic Programming (QP) algorithms, the tube-based tools, the set-constrained procedures, the Nonlinear Programming procedures and the robust ones; the main features of the recent research body on this topic are examined. A simulation example is given comparing some of the important techniques. Finally, some suggestions are given for future investigation threads, seeking further applicability of these methods.

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The global COVID-19 pandemic (SARS-CoV-2 virus) is the defining health crisis of our century. Due to the absence of vaccines and drugs that can help to fight it, the world solution to control the spread has been to consider public social distance measures that avoids the saturation of the health system. In this context, we investigate a Model Predictive Control (MPC) framework to determine the time and duration of social distancing policies. We use Brazilian data in the period from March to May of 2020. The available data regarding the number of infected individuals and deaths suffers from sub-notification due to the absence of mass tests and the relevant presence of the asymptomatic individuals. We estimate variations of the SIR model using an uncertainty-weighted Least-Squares criterion that considers both nominal and inconsistent-data conditions. Moreover, we add to our versions of the SIR model an additional dynamic state variable to mimic the response of the population to the social distancing policies determined by the government that affects the speed of COVID-19 transmission. Our control framework is within a mixed-logical formalism, since the decision variable is forcefully binary (the existence or the absence of social distance policy). A dwell-time constraint is included to avoid harsh shifting between these two states. Finally, we present simulation results to illustrate how such optimal control policy would operate. These results point out that no social distancing should be relaxed before mid August 2020. If relaxations are necessary, they should not be performed before the beginning this date and should be in small periods, no longer than 25 days. This paradigm would proceed roughly until January/2021. The second peak of infections, which has a forecast to the beginning of October, can be reduced if the periods of no-isolation days are