论文标题
两级晶格神经网络架构，用于控制非线性系统
Two-Level Lattice Neural Network Architectures for Control of Nonlinear Systems
论文作者
论文摘要
在本文中，我们考虑了自动设计一个整流的线性单元（RELU）神经网络（NN）体系结构（每层层和神经元数），并保证它足够参数以控制非线性系统。尽管当前的最新技术是基于手工挑选的架构或基于启发式的搜索以找到此类nn体系结构的，但我们的方法利用了给定的系统模型来设计体系结构。结果，我们提供保证，所得的NN体系结构足以实现满足可实现规范的控制器。我们的方法利用了两个基本思想。首先，假设该系统可以由一个未知的Lipschitz连续反馈控制器控制，一些Lipschitz和一些由$ k_ \ text {cont} $持续限制的lipschitz绑定了构建连续的分段仿射（CPWA）函数所需的仿射功能的数量，从而可以近似不知名的Lipschitz-chitz-Contininiuminulectiuncounterer。其次，我们利用了作者的最新结果，对新的NN体系结构称为两级晶格（TLL）NN体系结构，该体系结构被证明能够仅凭了解损害此CPWA功能的仿射功能的数量就可以实现任何CPWA功能。
In this paper, we consider the problem of automatically designing a Rectified Linear Unit (ReLU) Neural Network (NN) architecture (number of layers and number of neurons per layer) with the guarantee that it is sufficiently parametrized to control a nonlinear system. Whereas current state-of-the-art techniques are based on hand-picked architectures or heuristic based search to find such NN architectures, our approach exploits the given model of the system to design an architecture; as a result, we provide a guarantee that the resulting NN architecture is sufficient to implement a controller that satisfies an achievable specification. Our approach exploits two basic ideas. First, assuming that the system can be controlled by an unknown Lipschitz-continuous state-feedback controller with some Lipschitz constant upper-bounded by $K_\text{cont}$, we bound the number of affine functions needed to construct a Continuous Piecewise Affine (CPWA) function that can approximate the unknown Lipschitz-continuous controller. Second, we utilize the authors' recent results on a novel NN architecture named as the Two-Level Lattice (TLL) NN architecture, which was shown to be capable of implementing any CPWA function just from the knowledge of the number of affine functions that compromises this CPWA function.
