A controller based on neuro-dynamic programming coupled with a fuzzy ARTMAP neural network for a fed-batch bioreactor was developed to produce cloned invertase in Saccharomyces cerevisiae yeast in a fed-batch bioreactor. The objective was to find the optimal glucose feed rate profile needed to achieve the highest fermentation profit in this reactive system where the enzyme expression is repressed at high glucose concentrations. The controller updated in time an optimal control action that incremented the fed-batch bioreactor profitability. The proposed neuro-dynamic programming (NDP) approach, coupled with fuzzy ARTMAP classifier, utilized suboptimal control policies to start the optimization. The fuzzy ARTMAP algorithm was used to build a cost surface in the state space visited by the process, thus minimizing the curse of dimensionality with the associated high computational costs. Bellman's iteration was used to improve the fuzzy ARTMAP approximation of the cost surface before its implementation into the control system. The controller was tested at different fermentation conditions for initial reactor volumes within the range 0.4-0.81 and a final constant fermentation volume of 1.21. Profits were higher than those previously reported in the literature, with continuous and smooth glucose feed rate profiles easy to implement under production conditions. The control system was also tested when the substract concentration changed unexpectedly. The controller global performance was also in this case better than those obtained with the best suboptimal policy and previous methods. (c) 2006 Elsevier Ltd. All rights reserved.