The dynamics of fermentation processes are very complex and not completely known. Some state variables are non- measurable, and the process parameters are strongly time dependent. Recently, there are some control methods like fuzzy learning and neural networks, which are promising in dealing with non-linearity, complexity, and uncertainly of these processes. These methods are suitable for the modelling of these systems, which are difficult to describe mathematically. The fuzzy learning methods are useful for the modelling, they are less demanding on the mathematical model and a priori knowledge about the processes. Different techniques for estimating the state variables (that are non-measurable) in the fermentation process have been investigated. A non-linear auto-regressive with exogenous input (NARX) model was developed using process data from a pilot bioreactor. The fermentation process is splitted into three phases, where each phase was treated separately. Generally, fuzzy models have a capability of dividing an input space into several subspaces (fuzzy clustering), where each subspace is supposed to give a local linear model. In our work, we used global learning where the local models are less interpretable, but the global model accuracy is satisfying, and the fuzzy partition matrix is obtained by applying the Gustafson-Kessel algorithm. The fermentation parameters are estimated for a batch and a fed-batch culture. The number of inputs to our fuzzy model are three for a first simulation. We used four inputs for a second simulation, in order to detect some correlations among inputs. The results show that estimated parameters are close to the measured (or calculated) ones. The parameters used in the computation are identified using batch experiments .

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[17] Taibi M., Charef C., and Vincent N., “Identification of a Batch Fermentation Process,” International Conference on Geometric Modelling and Graphics , GMAG 03, London, UK, 2003. Mahmoud Taibi received his BSc in electrical engineering from USTO University, Oran, Algeria in 1980, then MSc from Badji-Mokhtar University, Annaba, Algeria in 1996. Currently, he is an assistant professor at Badji-Mokhtar University, Annaba, Algeria since 1983. His interests are in intelligent systems. Chabbi Charef received his BSc in electrical engineering from USTO University, Oran, Algeria in 1981, then MSc from Ohio University, Athens, Ohio USA in 1985, and he is preparing his PhD in electrical engineering. Currently, he is an assistant professor at Badji Mokhtar University, Annaba, Algeria since 1988. Nicole Vincentis a former student of L’Ecole Normale Supérieure, she got aggregation in mathematics, and defended a PhD in computer science at INSA de Lyon in 1988. She is a professor in computer science since 1996. Currently, she teaches at the University René Descartes Paris5. She is in charge for the SIP (Intelligent Systems of Perception) team of the Research Center in Information Sciences of Paris5, and is specialized in pattern recognition and image analysis.