Numerical algorithms for solving the optimal control problem of simple bioreactors

Abstract

The modified nonlocal feedback controller is used to control the production of drugs in a simple bioreactor. This bioreactor is based on the enzymatic conversion of substrate into the required product. The dynamics of this device is described by a system of two nonstationary nonlinear diffusion–convection–reaction equations. The analysis of the influence of the convection transport is one the aims of this paper. The control loop is defined using the relation, which shows how the amount of the drug produced in the bioreactor and delivered into a human body depends on the substrate concentration specified on the external boundary of the bioreactor. The system of PDEs is solved by using the finite volume and finite difference methods, the control loop parameters are defined from the analysis of stationary linearized equations. The second aim of this paper is to solve the inverse problem and to determine optimal boundary conditions. These results enable us to estimate the potential accuracy of the proposed devices.