Discrete-time MPC for switched systems with applications to biomedical problems

This paper studies switched systems in which the manipulated control action is the time-depending switching signal. To control the switched systems 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. Applications to schedule therapies in viral infection and cancer treatments are studied. The numerical results suggest that the proposed strategy outperforms the schedule for available treatments.