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Department of Electrical and Computer Engineering

Summary: Department of Electrical and
Computer Engineering
School of Engineering
University of New Mexico
A Synthesis of Gradient and Hamiltonian Dynamics Applied to
Learning in Neural Networks
James W. Howse Chaouki T. Abdallah Gregory L. Heileman
Department of Electrical and Computer Engineering
University of New Mexico
Albuquerque, NM 87131
UNM Technical Report Number: EECE95 003
Current Date: July 27, 1995
The processof model learningcan be considered in twostages: model selection and parameterestimation.
In this paper a technique is presented for constructing dynamical systems with desired qualitative
properties. The approach is based on the fact that an n-dimensional nonlinear dynamical system can
be decomposed into one gradient and n , 1 Hamiltonian systems. Thus, the model selection stage
consists of choosing the gradient and Hamiltonian portions appropriately so that a certain behavior is
obtainable. To estimate the parameters, a stably convergent learning rule is presented. This algorithm
is proven to converge to the desired system trajectory for all initial conditions and system inputs. This


Source: Abdallah, Chaouki T- Electrical and Computer Engineering Department, University of New Mexico


Collections: Engineering