Optimal control problems appear in several engineering fields and in particular on the control of fedbatch
fermentation processes. These problems are often described by sets of nonlinear differential and algebraic
equations, usually subject to constraints in the state and control variables.
Tradicional approaches to the optimal feed trajectory computation consists in getting a linear spline that approximates
the trajectory, which optimizes a given performance of the fed-batch fermentation process. This approach
leads to non-differentiable trajectories that can pose some problems to implement in practice, resulting in a possible
discrepancy of the simulated and real performances.
In this paper we develop a technique to obtain a cubic spline for the approximate trajectory, leading to a smooth
approximation function. We provide numerical results for a set of case studies where the AMPL modeling language,
CVODE ordinary differential equations solver and a particle swarm algorithm were used.Algoritmi Research Center.Fundação para a Ciência e a Tecnologia (FCT)