Comparative study of interpolating function in CVP based optimal control solutions of Fed-Batch Reactors

Abstract

Piecewise constant and piecewise linear are the most popular interpolating functions in Control Vector Parameterization (CVP) approach for solving optimal control problems. There has been significant impact of the choice of these interpolating functions on the optimal control problem solutions. These two interpolating functions are associated with sharp change of slopes of the control variables. This phenomenon may adversely affect the metabolism of the cells, which can subsequently result in decrease of the productivity.

This problem is overcome by the cubic spline interpolating function because of its smooth interpolation property. A detailed comparative study of various interpolating functions, namely piecewise constant, piecewise linear, and cubic spline trial functions has been presented in this work. Three popular case studies have been chosen for this purpose, namely penicillin, ethanol and secreted protein production in fed-batch reactors from glucose.