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

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 adaptation laws for the weights of each layer of a ResNet-based adaptive controller. A nonsmooth Lyapunov-based analysis is provided to guarantee global asymptotic tracking error convergence.