  Switched systems in which the manipulated control action is the
time-depending switching signal describe many engineering problems, mainly
related to biomedical applications. In such a context, to control the system
means to select an autonomous system - at each time step - among a given finite
family. Even when this selection can be done by solving a Dynamic Programming
(DP) problem, such a solution is often difficult to apply, and state/control
constraints cannot be explicitly considered. In this work a new set-based Model
Predictive Control (MPC) strategy is proposed to handle switched systems in a
tractable form. The optimization problem at the core of the MPC formulation
consists in an easy-to-solve mixed-integer optimization problem, whose solution
is applied in a receding horizon way. Two biomedical applications are simulated
to test the controller: (i) the drug schedule to attenuate the effect of viral
mutation and drugs resistance on the viral load, and (ii) the drug schedule for
Triple Negative breast cancer treatment. The numerical results suggest that the
proposed strategy outperform the schedule for available treatments.
