Nesterov-Accelerated Concurrent Learning for Lyapunov-Based Deep Neural Networks

Abstract

Concurrent learning (CL) has recently been extended to Lyapunov-based deep neural networks (DNNs) to obtain parameter convergence under finite rather than persistent excitation. However, the existing first-order law converges slowly, especially for high-dimensional systems and overparameterized networks. To address this problem, this paper develops a Nesterov-accelerated concurrent learning (NACL) adaptation law for uncertain second-order control-affine systems. The developed law drives momentum dynamics with recorded state-input data, so that all hidden layers of the DNN are updated online under a verifiable finite excitation condition. A dynamic state-derivative observer is designed to reconstruct the recorded input without acceleration measurements. The momentum variable introducesa cross term coupling the momentum lag error to the state-dependent DNN Jacobian and the tracking error, and a state-dependent normalization is introduced into the momentum filter to dominate it. A Lyapunov-based analysis establishes exponential convergence of the tracking, momentum, observer, and weight estimation errors to a bounded residual ball. Simulations on a six- degree-of-freedom unmanned underwater vehicle demonstrate a 24.5% and 62.9% reduction in the root-mean-square function approximation error relative to first-order CL and to a higher-order tuner without CL, respectively.