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Verification in the Loop: Correct-by-Construction Control Learning with Reach-avoid Guarantees
arXiv - CS - Formal Languages and Automata Theory Pub Date : 2021-06-06 , DOI: arxiv-2106.03245
Yixuan Wang, Chao Huang, Zhaoran Wang, Zhilu Wang, Qi Zhu

In the current control design of safety-critical autonomous systems, formal verification techniques are typically applied after the controller is designed to evaluate whether the required properties (e.g., safety) are satisfied. However, due to the increasing system complexity and the fundamental hardness of designing a controller with formal guarantees, such an open-loop process of design-then-verify often results in many iterations and fails to provide the necessary guarantees. In this paper, we propose a correct-by-construction control learning framework that integrates the verification into the control design process in a closed-loop manner, i.e., design-while-verify. Specifically, we leverage the verification results (computed reachable set of the system state) to construct feedback metrics for control learning, which measure how likely the current design of control parameters can meet the required reach-avoid property for safety and goal-reaching. We formulate an optimization problem based on such metrics for tuning the controller parameters, and develop an approximated gradient descent algorithm with a difference method to solve the optimization problem and learn the controller. The learned controller is formally guaranteed to meet the required reach-avoid property. By treating verifiability as a first-class objective and effectively leveraging the verification results during the control learning process, our approach can significantly improve the chance of finding a control design with formal property guarantees. This is demonstrated via a set of experiments on both linear and non-linear systems that use model-based or neural network based controllers.

中文翻译:

循环中的验证:具有到达避免保证的按构造控制学习

在安全关键自主系统的当前控制设计中,通常在设计控制器以评估是否满足所需属性(例如,安全性)之后应用形式验证技术。然而,由于系统复杂性的增加以及设计具有形式保证的控制器的基本难度,这种设计然后验证的开环过程经常导致多次迭代并且无法提供必要的保证。在本文中,我们提出了一种正确的构造控制学习框架,该框架以闭环方式将验证集成到控制设计过程中,即边设计边验证。具体来说,我们利用验证结果(系统状态的计算可达集)来构建控制学习的反馈指标,衡量当前控制参数设计满足安全和目标达成所需的避让属性的可能性。我们基于这些指标制定了一个优化问题来调整控制器参数,并使用差分方法开发近似梯度下降算法来解决优化问题并学习控制器。学习到的控制器被正式保证满足所需的避让属性。通过将可验证性视为一流目标并在控制学习过程中有效利用验证结果,我们的方法可以显着提高找到具有形式属性保证的控制设计的机会。这是通过对使用基于模型或基于神经网络的控制器的线性和非线性系统进行的一组实验来证明的。
更新日期:2021-06-08
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