A TP-LPV-LMI based control for Tumor Growth Inhibition

Abstract

Abstract The paper investigates the applicability of an advanced modern control method related to control of tumor growth under angiogenic inhibition. In order to describe the physiological process, a simple mathematical model was applied consisting of two states, the volume of the tumor and the inhibitor value. Extended Kalman Filter (EKF) was applied to estimate the unmeasurable state (inhibitor level). Linear Parameter Varying (LPV) models are used both at controller design (difference based control oriented LPV model) and EKF development (LPV model) level as well. We have used the Tensor Product (TP) model transformation accompanied by Linear Matrix Inequality (LMI) based optimization method in order to design a Parallel Distributed Compensator (PDC) kind TP-LPV-LMI controller considering additive disturbances (on both states) and sensor noise as well. Despite the assumed unfavorable effects the TP-LPV-LMI controller performed well achieving low final tumor volume and less totally injected inhibitor level.