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Lyapunov functions for rotor neural networks

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1 Author(s)
I. M. Elfadel ; Res. Lab. of Electron., MIT, Cambridge, MA, USA

The state of a rotor neuron is constrained to live on the surface of a sphere in ℜn. A rotor neural network is used to minimize an arbitrary cost function with respect to these "spherical" states. One practical example of such a situation is optimal charge distribution on a sphere in electromagnetism. In this paper, I show that if the cost function is quadratic in the neuron states, the synchronous, iterated-map algorithm used to find the fixed-points of the network has a Lyapunov function. I also propose a continuous-time dynamical system for finding the fixed-points, that is valid for any cost function. Moreover, I show that this continuous-time dynamics has a Lyapunov function. Finally, I show that a similar continuous-time algorithm and a similar Lyapunov function can be used for solving fixed-point equations more general than those of rotor neural networks.

Published in:

American Control Conference, 1994  (Volume:3 )

Date of Conference:

29 June-1 July 1994