Constrained control approach for monotone systems: application to tumour chemotherapy

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.