Supervised learning of perceptron and output feedback dynamic networks: a feedback analysis via the small gain theorem

This paper provides a time-domain feedback analysis of the perceptron learning algorithm and of training schemes for dynamic networks with output feedback. It studies the robustness performance of the algorithms in the presence of uncertainties that might be due to noisy perturbations in the reference signals or due to modeling mismatch. In particular, bounds are established on the step-size parameters in order to guarantee that the resulting algorithms will behave as robust filters. The paper also establishes that an intrinsic feedback structure can be associated with the training schemes. The feedback configuration is motivated via energy arguments and is shown to consist of two major blocks: a time-variant lossless (i.e., energy preserving) feedforward path and a time-variant feedback path. The stability of the feedback structure is then analyzed via the small gain theorem, and choices for the step-size parameter in order to guarantee faster convergence are deduced by using the mean-value theorem. Simulation results are included to demonstrate the findings.