Stochastic Deep Model Reference Adaptive Control

TL;DR

This paper introduces a stochastic deep neural network-based adaptive control method that models uncertainties and non-linearities, ensuring real-time boundedness and convergence through Bayesian learning and Lyapunov-based adaptation.

Contribution

It extends previous deep model reference adaptive control by integrating Bayesian DNNs for uncertainty quantification and real-time adaptive weight updates.

Findings

Ensures boundedness and guaranteed tracking performance.

Provides confidence intervals over predictions using Bayesian DNNs.

Achieves convergence through induced persistency of excitation.

Abstract

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.