Recent research has shown that supervised learning can be an effective tool for designing optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of these neural network (NN) controllers is still not well understood. In this paper we use numerical simulations to demonstrate that typical test accuracy metrics do not effectively capture the ability of an NN controller to stabilize a system. In particular, some NNs with high test accuracy can fail to stabilize the dynamics. To address this we propose two NN architectures which locally approximate a linear quadratic regulator (LQR). Numerical simulations confirm our intuition that the proposed architectures reliably produce stabilizing feedback controllers without sacrificing performance. In addition, we introduce a preliminary theoretical result describing some stability properties of such NN-controlled systems.

翻译：最近的研究显示,有监督的学习可以成为设计高维非线性动态系统最佳反馈控制器的有效工具。 但是,这些神经网络控制器的行为仍然没有得到很好的理解。 在本文中,我们使用数字模拟来证明典型的测试精确度指标无法有效捕捉NN控制器稳定系统的能力。 特别是,一些测试精度高的NN不能稳定动态。 为了解决这个问题,我们提议了两个本地接近线性二次调节器(LQR)的NN结构。 数字模拟证实了我们的直觉,即拟议的结构可以可靠地产生稳定的反馈控制器而不牺牲性能。 此外,我们引入了一个初步理论结果,描述了这类NNN控制系统的某些稳定性特性。