Constrained control approach for monotone systems: application to tumour chemotherapy

Abstract

Monotone systems are dynamical systems whose solutions preserve an ordering relative to the initial data. This study develops a set-point regulation approach for a certain class of systems subject to input and state constraints which leads to closed-loop strongly monotone systems. The proposed method gives static output feedback controllers that guarantee the convergence of generic bounded solutions to the desired set-point, satisfy the constraints and preserve the control performance under the input saturation. Although such a set-point regulation problem is too challenging for general non-linear systems, the proposed approach finds some well-organised controllers that satisfy the mentioned control objectives. To investigate the applicability of the proposed control technique, the authors exploit a model of cancer tumour growth in an unhealthy tissue. The medication (control) intends to take solutions to the healthy state through a constrained chemotherapy protocol. The authors present a full dynamical analysis for this system.