Optimal input design for low-dimensional systems: An Haldane kinetics example

In this paper the well-known problem of optimal input design is considered. The problem is formulated as follows: given a dynamic non-linear model structure which is assumed to be affine in the input, and a specific parameter of interest θk, find a feedback law that maximizes the sensitivity of the model output to the parameter. Analytical solutions to this specific problem for a general single state model structure are presented. As an example a bioreactor with a biomass that grows according to the well-known Haldane kinetics under regulated biomass concentration is considered.