Singular Optimal Control of Fed-batch Fermentation Processes with State Inequality Constraints

Abstract

We consider the design of a substrate feed rate controller for a class of biotechnical processes in stirred tank reactors characterized by growth/production decoupling, for the most common case of monotonic specific growth rate and non-monotonic specific production rate. With the volumetric substrate feed rate as the manipulated variable, this yields a singular optimal control problem. Due to state inequality constraints complete solutions are especially hard to obtain and almost nonexistent in the literature. However, the techniques proposed in the literature to convert the problem into a non-singular one all suffer from problems with respect to practical implementation. Therefore, we adopt the traditional singular control viewpoint. The algorithm presented has some marked advantages over algorithms reported in the literature. In addition, we present a complete general solution in the realistic case of input and state inequality constraints. This approach leads in a natural way to the design of robust optimal adaptive control strategies (Van Impe 1993).