Two-Level Lattice Neural Network Architectures for Control of Nonlinear Systems
Two-Level Lattice Neural Network Architectures for Control of Nonlinear Systems
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DOI：
10.1109/cdc42340.2020.9304079
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发表时间：
2020-04
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影响因子：
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通讯作者：
James Ferlez;Xiaowu Sun;Yasser Shoukry
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文献类型：
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作者：
James Ferlez;Xiaowu Sun;Yasser Shoukry
在本文中，我们考虑自动设计整流线性单元（ReLU）神经网络（NN）架构（层数和每层神经元数量）的问题，并保证其足够参数化以控制非线性系统。虽然当前最先进的技术基于手工挑选的架构或基于启发式的搜索来寻找此类神经网络架构，但我们的方法利用给定的系统模型来设计架构；因此，我们保证最终的神经网络架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，我们假设系统可以由 Lipschitz 连续状态反馈控制器控制，该控制器未知，但其 Lipschitz 常数的上限为已知常数；然后使用这个假设，我们限制了构造连续分段仿射 (CPWA) 函数所需的仿射函数的数量，该函数可以逼近未知的 Lipschitz 连续控制器。其次，我们利用了作者在两级格子 (TLL) 神经网络架构上的最新成果，这是一种新颖的神经网络架构，它被证明可以直接通过构成其实现的 CPWA 函数的仿射函数的数量进行参数化。我们还通过设计神经网络架构来控制倒立摆来评估我们的方法。
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 a 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, we assume that the system can be controlled by a Lipschitz-continuous state-feedback controller that is unknown but whose Lipschitz constant is upper-bounded by a known constant; then using this assumption, 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 the Two-Level Lattice (TLL) NN architecture, a novel NN architecture that was shown to be parameterized directly by the number of affine functions that comprise the CPWA function it realizes. We also evaluate our method by designing a NN architecture to control an inverted pendulum.