A Convex Parameterization of Robust Recurrent Neural Networks
A Convex Parameterization of Robust Recurrent Neural Networks
复制标题
鲁棒循环神经网络的凸参数化
DOI：
--
复制
发表时间：
2020
影响因子：
3
通讯作者：
I. Manchester
中科院分区：
文献类型：
--
作者：
Max Revay;Ruigang Wang;I. Manchester
递归神经网络(RNN)是一类常用于序列到序列映射建模的非线性动力系统。RNN具有出色的表达能力，但缺乏许多应用所必需的稳定性或健壮性保证。在这封信中，我们建立了具有稳定性和健壮性保证的RNN的凸集。这些保证是使用增量二次约束得到的，可以确保所有解的全局指数稳定性，以及增量$ell_{2}$增益(学习序列到序列映射的Lipschitz常数)的界。利用一种隐式模型结构，我们构造了一种关于模型参数和稳定性证明联合凸的RNN的参数化。我们证明了该模型结构包括了以前提出的所有稳定RNN的凸集作为特例，也包括了所有稳定的线性动力系统。数值实验表明了所提出的模型类在非线性系统辨识中的有效性。
Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many applications. In this letter, we formulate convex sets of RNNs with stability and robustness guarantees. The guarantees are derived using incremental quadratic constraints and can ensure global exponential stability of all solutions, and bounds on incremental $ell _{2} $ gain (the Lipschitz constant of the learned sequence-to-sequence mapping). Using an implicit model structure, we construct a parametrization of RNNs that is jointly convex in the model parameters and stability certificate. We prove that this model structure includes all previously-proposed convex sets of stable RNNs as special cases, and also includes all stable linear dynamical systems. Numerical experiments illustrate the utility of the proposed model class in the context of non-linear system identification.