Perceptron Training Algorithms designed using Discrete-Time Control Liapunov Functions

Perceptrons, proposed in the seminal paper McCulloch-Pitts of 1943, have remained of interest to neural network community because of their simplicity and usefulness in classifying linearly separable data. Gradient descent and conjugate gradient are two widely used techniques for solving a set of linear inequalities. In finite precision implementation, the numerical errors could cause a loss of the residue orthogonality, which, in turn, results in loss of convergence. This paper takes a recently proposed control-inspired approach, to the design of iterative perceptron training algorithms, by regarding certain training/algorithm parameters as controls and then using a control Liapunov technique to choose appropriate values of these parameters.