Lyapunov-Based Deep Residual Neural Network (ResNet) Adaptive Control

Deep Neural Network (DNN)-based controllers have emerged as a tool to compensate for unstructured uncertainties in nonlinear dynamical systems. A recent breakthrough in the adaptive control literature provides a Lyapunov-based approach to derive weight adaptation laws for each layer of a fully-connected feedforward DNN-based adaptive controller. However, deriving weight adaptation laws from a Lyapunov-based analysis remains an open problem for deep residual neural networks (ResNets). This paper provides the first result on Lyapunov-derived weight adaptation for a ResNet-based adaptive controller. A nonsmooth Lyapunov-based analysis is provided to guarantee asymptotic tracking error convergence. Comparative Monte Carlo simulations are provided to demonstrate the performance of the developed ResNet-based adaptive controller. The ResNet-based adaptive controller shows a 64% improvement in the tracking and function approximation performance, in comparison to a fully-connected DNN-based adaptive controller.