  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.
