Output Zeroing within a Hopfield Network

Abstract

In this paper we investigate a specific problem from the control theory literature, that of zeroing a system output, from the point of view of a neural network. For this we consider functions of the neural network states as defining a system output. In particular we are concerned with a continuous network of Hopfield type which could, in theory, be manufactured with available electrical components. Our aim is to impose a specific dynamics on a network by calculating the synaptic weights directly, without requiring training. Hence when a network is initialised in certain states we can be confident that the functions defining the output will remain sufficiently close to zero. We use (nonlinear) geometrical methods in our analysis and reliable numerical methods for our computations.