Neural networks are typically sensitive to small input perturbations, leading
to unexpected or brittle behaviour. We present RobustNeuralNetworks.jl: a Julia
package for neural network models that are constructed to naturally satisfy a
set of user-defined robustness constraints. The package is based on the
recently proposed Recurrent Equilibrium Network (REN) and Lipschitz-Bounded
Deep Network (LBDN) model classes, and is designed to interface directly with
Julia's most widely-used machine learning package, Flux.jl. We discuss the
theory behind our model parameterization, give an overview of the package, and
provide a tutorial demonstrating its use in image classification, reinforcement
learning, and nonlinear state-observer design.

RobustNeuralNetworks.jl 是一个在 Julia 构建的神经网络模型的包，旨在自然满足一组用户定义的的鲁棒性约束，其基于 Recurrent Equilibrium Network (REN) 和 Lipschitz-Bounded Deep Network (LBDN) 模型类并与 Julia 最广泛使用的机器学习包 Flux.jl 直接交互，并演示了包的概述和在图像分类，增强学习和非线性状态观察器设计中使用的教程。

RobustNeuralNetworks.jl：一个具有认证鲁棒性的机器学习和数据驱动控制软件包

RobustNeuralNetworks.jl: a Package for Machine Learning and Data-Driven  Control with Certified Robustness

We propose a parameterization of a nonlinear dynamic controller based on the
recurrent equilibrium network, a generalization of the recurrent neural
network. We derive constraints on the parameterization under which the
controller guarantees exponential stability of a partially observed dynamical
system with sector bounded nonlinearities. Finally, we present a method to
synthesize this controller using projected policy gradient methods to maximize
a reward function with arbitrary structure. The projection step involves the
solution of convex optimization problems. We demonstrate the proposed method
with simulated examples of controlling nonlinear plants, including plants
modeled with neural networks.

基于循环平衡网络的非线性动态控制器参数化方法，通过投影策略梯度方法来合成控制器，并解决系统的快速稳定性与非线性问题。