Towards Interpretable Inverse Model Control: The Role of Grey-Box Models

This work presents and compares two approaches for inverse modelling and control of a biotechnological system: a fuzzy rule-based model and a Kolmogorov–Arnold network (KAN) model. Both approaches aim to derive a control law that enables the system to reach a desired substrate concentration through model inversion. Whereas the fuzzy model offers interpretability via linguistic rules, the KAN model provides an explicit functional representation that allows for the analysis and visualisation of individual input contributions through univariate functions. It is shown how both models can be inverted online to determine the required dilution rate, thereby generating controlled trajectories that remain close to the reference signal. The results indicate that the use of interpretable models is viable for control applications and, in addition, may provide advantages in terms of transparency, pruning capability, and the automatic generation of symbolic expressions. These features can assist in determining or adapting implementations in critical control systems. Smart citations: https://scite.ai/reports/10.61467/2007.1558.2026.v17i1.1244 Dimensions.Open Alex.