论文标题
REACH-SDP：通过半决赛编程与神经网络控制器对闭环系统的可及性分析
Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming
论文作者
论文摘要
在闭环控制系统中使用神经网络以提高性能并降低在线实施的计算成本方面，人们对使用神经网络产生了越来越多的兴趣。但是，由于神经网络的非线性和组成结构，为这些系统提供安全性和稳定性保证是具有挑战性的。在本文中，我们提出了一种新型的远期可及性分析方法，用于使用反馈互连的神经网络对线性时变系统的安全验证。我们的技术方法依赖于通过二次约束来抽象非线性激活函数，从而导致闭环系统的前向触及式集合的外部相关性。我们表明，我们可以使用半决赛编程来计算这些近似可及的集合。我们在四键示例中说明了我们的方法，其中我们首先通过深神经网络近似非线性模型预测控制器，然后应用我们的分析工具来证明有限的时间到达性能和闭环系统的约束满意度。
There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these systems is challenging due to the nonlinear and compositional structure of neural networks. In this paper, we propose a novel forward reachability analysis method for the safety verification of linear time-varying systems with neural networks in feedback interconnection. Our technical approach relies on abstracting the nonlinear activation functions by quadratic constraints, which leads to an outer-approximation of forward reachable sets of the closed-loop system. We show that we can compute these approximate reachable sets using semidefinite programming. We illustrate our method in a quadrotor example, in which we first approximate a nonlinear model predictive controller via a deep neural network and then apply our analysis tool to certify finite-time reachability and constraint satisfaction of the closed-loop system.
