A neural network for N-stage optimal control problems

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 backpropagation. In this paper a particular neural network to 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 Bellmann´s optimality principle and on 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 absence of exhaustive training. Some important applications are addressed to illustrate the usefulness of the approach proposed