  A control theoretic approach is presented in this paper for both batch and
instantaneous updates of weights in feed-forward neural networks. The popular
Hamilton-Jacobi-Bellman (HJB) equation has been used to generate an optimal
weight update law. The remarkable contribution in this paper is that closed
form solutions for both optimal cost and weight update can be achieved for any
feed-forward network using HJB equation in a simple yet elegant manner. The
proposed approach has been compared with some of the existing best performing
learning algorithms. It is found as expected that the proposed approach is
faster in convergence in terms of computational time. Some of the benchmark
test data such as 8-bit parity, breast cancer and credit approval, as well as
2D Gabor function have been used to validate our claims. The paper also
discusses issues related to global optimization. The limitations of popular
deterministic weight update laws are critiqued and the possibility of global
optimization using HJB formulation is discussed. It is hoped that the proposed
algorithm will bring in a lot of interest in researchers working in developing
fast learning algorithms and global optimization.
