An application of Hamiltonian neurodynamics using Pontryagin's maximum (minimum) principle

Hamiltonians can generate Artificial Neural Dynamical systems dependent on time. Classical methods from optimal control theory, notably Pontryagin's Maximum (Minimum) principle (PMP) can be employed, together with Hamiltonians, in order to determine the optimal weights. Today, although several extended-backpropagation methods using optimization theory have been developed based on the well known standard backpropagation algorithm (SBP), feedforward multilayer perceptron (MLP) neural networks are here employed on differential equations which have characteristics such as admitting neurons and time dependent weight vectors . In this thesis, it is shown that the PMP learning rule obtained using PMP compares favourably with SBP. As a result, the PMP learning rule provides new results with feedforward networks; it can also be applied to recurrent networks, in both continuous-time and discrete-time.