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

TL;DR

This paper introduces a set-based Model Predictive Control approach for switched systems, enabling effective control in biomedical applications like viral load management and cancer treatment, with improved performance over existing schedules.

Contribution

A novel, tractable MPC strategy using mixed-integer optimization for switched systems with applications in biomedical treatment scheduling.

Findings

Outperforms existing treatment schedules in simulations.

Handles state and control constraints explicitly.

Applicable to complex biomedical control problems.

Abstract

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.