Output Zeroing within a Hopfield Network
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.
KeywordsEquilibrium Point Output Function Synaptic Weight Maximal Rank Computing Element
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- Isidori, A. ‘Nonlinear Control Systems’ 2nd edition, Springer-Verlag, 1989.Google Scholar
- Gallot, S., Hulin, D. and Lafontaine, J. ‘Riemannian Geometry’ Springer-Verlag, 1987.Google Scholar
- Olver, P.J. ‘Applications of Lie Groups to Differential Equations’ Springer-Verlag, 1986.Google Scholar
- Golub, G.H. and Van Loan, C.F. ‘Matrix Computations’ North Oxford Academic, 1983.Google Scholar