Constrained RMPC algorithms for time delay systems with parametric uncertainties: Application to the cancer combined therapy

摘要

In this paper, a new MPC formulation for systems with known delayed states and a new iterative algorithm of robust model predictive control (RMPC) subject to polytopic-type parameter uncertainties and input constraints is presented. Control of delayed systems with parameter uncertainties is usually more complicated in presence of input constraints. MPC is an appropriate approach to handle this type of problems. Unlike existing MPC techniques, the main advantage of the proposed MPC algorithms is that they are simple to construct and therefore can be simply implemented in real applications. Combined chemotherapy and anti-angiogenic treatment is a novel medical approach used for cancer treatment in recent years. The paper shows the performance of proposed algorithms for tumor volume reduction in combined therapy subject to the necessary constraints on drugs dosage. In order to be more realistic, we consider model with delays in states that describe the process of angiogenesis-the growth of new blood vessels by budding from pre-existing vessels - and uncertainty in parameters. Finally, the simulation results illustrate the performance of the proposed algorithms.