发表机构
Louisiana State University（路易斯安那州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Nesterov加速的并发学习自适应法则，用于基于Lyapunov的深度神经网络，以加速参数收敛，并在无人水下航行器仿真中显著降低逼近误差。
AI 中文摘要
并发学习（CL）最近被扩展到基于Lyapunov的深度神经网络（DNNs），以在有限激励而非持续激励下获得参数收敛。然而，现有的一阶法则收敛缓慢，特别是对于高维系统和过参数化网络。为了解决这个问题，本文针对不确定的二阶控制仿射系统，开发了一种Nesterov加速的并发学习（NACL）自适应法则。所开发的法则利用记录的状态-输入数据驱动动量动力学，使得DNN的所有隐藏层在可验证的有限激励条件下在线更新。设计了一个动态状态导数观测器，以在没有加速度测量的情况下重构记录输入。动量变量引入了一个交叉项，将动量滞后误差与状态相关的DNN雅可比矩阵和跟踪误差耦合，并在动量滤波器中引入了状态相关的归一化以主导该交叉项。基于Lyapunov的分析建立了跟踪、动量、观测器和权重估计误差指数收敛到有界残差球。在六自由度无人水下航行器上的仿真表明，相对于一阶CL和无CL的高阶调节器，均方根函数逼近误差分别减少了24.5%和62.9%。
英文摘要
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.
