An application of Hamiltonian neurodynamics using Pontryagin's Maximum (Minimum) Principle.

Classical optimal control methods, notably Pontryagin's Maximum (Minimum) Principle (PMP) can be employed, together with Hamiltonians, to determine optimal system weights in Artificial Neural dynamical systems. A new learning rule based on weight equations derived using PMP is shown to be suitable for both discrete- and continuous-time systems, and moreover, can also be applied to feedback networks. Preliminary testing shows that this PMP learning rule compares favorably with Standard BackPropagations (SBP) on the XOR problem.