Switched NMPC for epidemiological and social-economic control objectives in SIR-type systems

Several optimal control strategies have recently been developed to minimize the infected peak prevalence or the epidemic final size. Although these two indexes are critical to assess any control policy tending to mitigate an epidemic by means of non-pharmaceutical measures, they are usually considered separately and, in general, no consensus has been reached about how to simultaneously handle them in a simple and realistic way (i.e., accounting for the limitations in the control actions, avoiding new cycles of infections or reboundings, considering side effects, etc.) Here, based on a theoretical dynamical analysis of SIR-type models, a realistic nonlinear model predictive control strategy is proposed. Apart from minimizing the epidemic final size and keeping the infected peak prevalence under an established value, the controller accounts for feedback uncertainty and different actuator constraints, such as a limited number of social distancing policies, which may remain active for a minimal and a maximal time interval. Several simulations considering different SIR-type models illustrate the benefits of the proposal.