On nonlinear continuous-time optimal control of penicillin cultivation

This paper presents continuous-time optimal control of penicillin production maximizing penicillin concentration at chosen final time. First, control input parametrization is performed and the input is expressed as a piece-wise affine function of continuous time reducing the number of optimizable parameters. Then, iterative numerical gradient optimization with the initial conditions corresponding to the optimal input obtained by projected gradient optimization is used to find the optimal values of the optimized parameters. The proposed approach is compared to both the original gradient method and the traditionally used classical nonlinear feedback controller. All these strategies are tested on a set of numerical experiments for various cultivation lengths and the results are evaluated and discussed. The comparison reveals significant superiority of the proposed algorithm. Together with impressive reduction of memory space needed to store the solution, the results improvement makes the proposed algorithm very attractive from the industrial point of view.