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

• Published in: arXiv.org
• Main Authors: Anderson, Alejandro, Gonzalez, Alejandro Hernan, Ferramosca, Antonio, Esteban Abelardo Hernandez Vargas
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 23.06.2020
• Subjects: Biomedical engineering; Biomedical materials; Computer simulation; Discrete time systems; Dynamic programming; Load resistance; Mathematics - Optimization and Control; Mutation; Optimization; Predictive control; Schedules
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2006.12936

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.