Feedback control of the COVID-19 outbreak based on active disturbance rejection control

The outbreak of COVID-19 causes a serious threat to human health and life around the world and puts enormous pressure on the healthcare system. The lockdown policy has effectively reduced the number of cases and suppressed the spread of the COVID-19 epidemic, but it also requires high social and economic costs. In this paper, we aim to use feedback control to help decision-makers establish lockdown policies, which can effectively constrain the spread of the COVID-19 pandemic with minimal financial loss. The time-dependent susceptible-infected-removed (SIR) model is used for the dynamics of the COVID-19 pandemic. The feedback control is based on a modified nonlinear active disturbance rejection controller (ADRC) that includes modified nonlinear extended state and nonlinear state error feedback with parameters tuned by particle swarm optimization, and the performances are compared with a well-known proportional--integral--derivative (PID) controller. The final simulation results show that the modified nonlinear ADRC has better performances and is more robust against uncertainties in the parameters of the epidemiological model.