  In this paper, we present a Stochastic Deep Neural Network-based Model
Reference Adaptive Control. Building on our work "Deep Model Reference Adaptive
Control", we extend the controller capability by using Bayesian deep neural
networks (DNN) to represent uncertainties and model non-linearities. Stochastic
Deep Model Reference Adaptive Control uses a Lyapunov-based method to adapt the
output-layer weights of the DNN model in real-time, while a data-driven
supervised learning algorithm is used to update the inner-layers parameters.
This asynchronous network update ensures boundedness and guaranteed tracking
performance with a learning-based real-time feedback controller. A Bayesian
approach to DNN learning helped avoid over-fitting the data and provide
confidence intervals over the predictions. The controller's stochastic nature
also ensured "Induced Persistency of excitation," leading to convergence of the
overall system signal.
