Robust Multi-Objective Singular Optimal Control Ofpenicillin Fermentation Process

Abstract

The determination of optimal feeding profile of fedbatch fermentation requires the solution of a singular optimal control problem. The complexity in obtaining the solution to this singular problem is due to the nonlinear dynamics of the system model, the presence of control variables in linear form and the existence of constraints in both the state and control variables. Traditionally, during the optimization process, uncertainties associated with design variables, control parameters and mathematical model are not considered. In this contribution, a systematic methodology to evaluate uncertainties during the resolution of a singular optimal control problem is proposed. This approach consists of the Multiobjective Optimization Differential Evolution algorithm associated with Effective Mean Concept. The proposed methodology is applied to determine the feed substrate concentration in fed-batch penicillin fermentation process. The robust multiobjective singular optimal control problem consists of maximizing the productivity and minimizing the operation total time. The overall profit is considered as a postprocessing criterion in the choice and implementation of a result contained in the Pareto set. The results obtained indicate that the proposed methodology represents an interesting approach to solve this kind of problem.