Equivalent Models, Maximum Principle and Optimal Control of Continuous Biotechnological Process: Peculiarities and Problems

Introduction The biosynthesis process description belongs to the class of non-linear, non-stationary, complex systems. The implementation of optimisation methods as well as Pontryagin’s maximum principle-based method is problematic when a non-linear model is used. A differential geometric technique permits the utilisation of a new non-linear transformation of a biotechnological kinetic model into an equivalent model. The model investigated in this paper permits exact linearization to the Brunovsky normal form. In certain cases this transformation technique allows to obtain an equivalent model, which substantially simplifies the mathematical derivations leading to the optimal control law. All these peculiarities, together with the complex formula of the latter dependence cause difficulties when implementing this differential geometric technique. However, in other cases this peculiarity becomes an advantage, which permits interesting new solutions. In this paper we discuss the possibilities for utilisation of these equivalent models in order to determine the optimal control solutions.