DEVELOPMENT OF A COMPUTER ALGORITHM-BASED ON A CONJUGATE-GRADIENT APPROACH FOR OPTIMIZATION OF FED-BATCH FERMENTATIONS

The problem of optimization of fed-batch fermentations using the subst rate feed rate as the control variable is singular in nature. Previous approaches, including the boundary condition iteration method and tra nsformation to a nonsingular problem using a different control variabl e, do not work well for solving optimization of systems governed by mo re than four differential equations. The applicability of a first-orde r conjugate gradient algorithm for optimizing fed-batch fermentations was tested for systems of varing complexity. This approach does not ne ed any variable transformation or a priori knowledge of the control ar c sequence. Constraints on the feed rate are handled in a simple and d irect manner. The algorithm worked very well for three, four, and five -dimensional singular systems. The correctness of the optimal profile was judged by observing the variation in the sign of the gradient of t he Hamiltonian. The gradient was found to be zero during the singular period and had the appropriate sign on the boundary arcs. The optimiza tion method based on conjugated gradient approach can be complementary to the boundary condition iteration method for determination of the e xact optimum profile.