Título: Dynamic Optimization Applied to Fed-Batch Fermentation with Phases Identification.
Autores: LOBATO, F. S.
Revista: International Review of Chemical Engineering - Rapid Communications (IRECHE), 5, 11-20, 2013.
Resumo: The determination of optimal substrate feed rate in bioreactors characterize an Optimal Control Problem (OCP) with singular control, where the control variable appears linearly both in the dynamic equations describing the process and/or in the objective function. Several numerical methods have been proposed in the literature to solve OCP, between them, the Pontryagin's Minimum Principle (PMP) approach is based on the optimal control theory and requires the numerical solution of boundary value problems involving state and adjoint (costate) variables. The main disadvantage of this strategy is the initial estimate for the costate variables. In this contribution, the dependence of the costate variables is eliminated from the differential-algebraic system of equations though the transformation of the original OCP into a problem of phases identification of fluctuating differential index and the transition instants in which they occur. The proposed methodology is applied to two classical cases involving restrictions in the productivity, in the control variable and in the bioreactor volume, for operation with final free time.

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