Tensor Product Model Transformation-based Parallel Distributed Control of Tumor Growth

Abstract

The current work investigates tumor growth control under antiangiogenic targeted molecular therapy by use of Tensor Product (TP) transformation. During the dynamics of the tumor growth we have considered that the tumor volume x 1 (t) is measurable, while due to the lack of information about the second state x 2 (t) (the inhibitor level in the serum), we have developed an appropriate Extended Kalman Filter (EKF) to estimate it. We applied different quasi Linear Parameter Varying (qLPV) models during the design of the EKF and the controller. Tensor Product model transformation method completed with Linear Matrix Inequality based optimization have been applied to design the main controller. The reference signals were generated by trajectory tracking kind control based on Inverse Dynamic Control-Proportional Derivate compensator, applied it on the "simulated" (original) model. We did not consider any state disturbance. However, we have taken into account sensor noise in accordance with the properties of the model. We have found that all of the control goals have been satisfied with the developed control framework: (i) the tumor volume was lower than 1 mm 3 at the end of the therapy; (ii) the developed models have approached each other with good accuracy; (iii) the totally injected inhibitor level was physiologically acceptable.