With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a trade-off has to be navigated. To address this issue, this paper proposes a method to generate an approximation of a neural network which is certifiably more robust. Crucially, the method is fully convex and posed as a semi-definite programme. An application to robustifying model predictive control is used to demonstrate the results. The aim of this work is to introduce a method to navigate the neural network robustness/accuracy trade-off.

翻译：随着神经网络被用于控制安全关键系统，其不仅需要具备准确性（即实现输入到输出的精确匹配），还必须满足鲁棒性要求。然而，这两种特性往往相互制约，需要权衡协调。针对这一问题，本文提出一种可生成具有可验证更强鲁棒性的神经网络近似模型的方法。该方法的核心优势在于完全凸化，并以半定规划形式构建。通过鲁棒模型预测控制的应用实例验证了该方法的有效性。本研究旨在提出一种能够平衡神经网络鲁棒性与准确性之间矛盾的系统性方法。