OPTIMIZATION OF DRUG THERAPY AND VIROTHERAPY WITH NONLINEAR MODEL THROUGH LINEAR PARAMETER VARYING (LPV) APPROACH - Putri Army, Dianita
Cancer is one of the biggest causes of death in the world and there is not yet found specific drugs to cure cancer. Treatment using drugs and virotherapy can be applied to treat cancer patients and this cancer treatment problem can be described as optimal control problem. The purpose of control is to increase the number of uninfected tumor cells and to decrease the number of infected tumor cells, with design control is the allocation of drug therapy and virotherapy doses. Model will be solved with Pontryagin’s Minimum Principle and from numerical simulation the results showed increasing of uninfected tumor cells and decreasing of infected tumor cells. Representatively, disturbance during virotherapy will be added to the model. Thus, the model is in a form of nonlinear mathematics model with disturbance. There are some methods to solve nonlinear model with disturbance, such as robust control, linearization or sliding mode. In this thesis, we will use Linear Parameter Varying (LPV) system to approach solution of nonlinear system with disturbance. First step in forming LPV system is transforming state variable, to trim nonlinear form. Second, choosing polytope in certain interval and designing vertex that correspond to its polytope. Third, constructing polytopic coordinate which satisfy conditions such as the value must be nonnegative and the total values is 1. Controller from LPV system will be obtained from linear combination of polytopic coordinate and controller in each vertex. This LPV controller is applied to nonlinear system of cancer treatment. Last, numerical simulation of LPV system showed that the number of uninfected tumor cells will increase to its carrying capacity and the number of infected tumor cells will decrease to 0 without drug therapy but will be given maximum doses of virotherapy every 10 days during therapy cycle.