Decentralized model reference adaptive control design for nonlinear systems; application to cancer treatment

Abstract

The paper gives an approach to decentralized Model Reference Adaptive Control (MRAC) design for nonlinear dynamical systems and illustrates the method with an application to cancer treatment. The nonlinear mathematical model of the cancer dynamics is described by a set of differential equations each of which defines the variation of different cell numbers. The model also includes the treatment effects which are specifically defined by immune, vaccine and chemotherapy. The proposed MRAC design methodology is based upon a stable nonlinear reference model which is produced by a state feedback controller using the so called State Dependent Riccati Equation (SDRE) techniques. The plant dynamics is nonlinear by nature and an adaptation methodology is designed such that response of the nonlinear reference model is followed. The adaptation is performed on a state dependent basis mainly using the adaptation mechanism designed for multi input multi output (MIMO) linear time invariant (LTI) systems. The proposed technique is illustrated to develop mixed immunotherapy, chemotherapy and vaccine therapy drug administration for cancer treatment using a tumor growth mathematical model. Simulation results show the effectiveness of the SDRE based MRAC for MIMO nonlinear systems.