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Abdract-Neural nets have the potential to be a powerful tool in dealing with nonlinear systems. Different approaches about how neural nets can be incorporated in optimal control strategies have been proposed in terms of general gradient descent and back-propagation. In this paper a particular neural network t o solve discrete time N-stage optimal control problems with a direct method to assign its weights is introduced, to systematically incorporate knowledge about the system's behavior. This method is based on the Bellmann's Optimality Principle and in the interchange of information which occurs during the synaptic chemical processing among neurons. This approach presents some advantages with regard to alternative approaches because of the ausence of exaustive training. Some important applications are addressed to illustrate the usefulness of the approach proposed. I. ~N T R O D U C T I O NThe need to meet demanding control requirements in increasingly complex dynamical systems under significant uncertainties makes neural networks very attractive because of their ability t o learn, t o approximate functions, to classify patterns and because of their potential for massively parallel hardware implementation [I].A number of different approaches for training a controller have been described in the literature. They include reinforcement leariling [2]. inverse control [ll], [I41 and optimal control [9], [ll]. Optimal control problems can be solved by dynamic programming techniques. However, because of t,he large con~putational requirements of the st.andard computational algorithm a number of new procedures with reduced computational requirements have been developed. *Supported by CNPq grant # 300634/925 'Supported by CNPq grant # 300?29/863 0-7803-1901-X/94 $4.00 01994 IEEE 4508 ~ Fernando GoinideRecently, an neural network with a two-layer feedback topology for solving discrete dynamic programming problems has been proposed [5]. The learning method iniplemented by this neural-network is equivalent. to the dynamic programming algorithni. A class of fuzzy decision making problems have also been solved by this approach [GI. In both in cases, Max and Min neuron models proposed in [8] have been utilized to construct the neural network.In this paper generalized recurrent neurons models are introduced from which the Max and Min neurons of [8] can be obtained. Based on this new neuron model a modification of the approach proposed in [5] is presented.

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SummaryThe modified simplex algorithm proposed by Nelder and Mead has been used to optimize the separation by temperature programmed capillary GC, of volatile compounds present in alcoholic beverages. An adequate objective function, CRF; based on the separation factor of Kaiser has been used for the optimization process.A factorial design was initially performed to verify the relationship between the several parameters of interest. Following this, the optimization was executed and a surface adjusted within the set of experimental data.