In large-scale networks of uncertain dynamical systems, where communication is limited and there is a strong interaction among subsystems, learning local models and control policies offers great potential for designing high-performance controllers. At the same time, the lack of safety guarantees, here considered in the form of constraint satisfaction, prevents the use of data-driven techniques to safety-critical distributed systems. This paper presents a safety framework that guarantees constraint satisfaction for uncertain distributed systems while learning. The framework considers linear systems with coupling in the dynamics and subject to bounded parametric uncertainty, and makes use of robust invariance to guarantee safety. In particular, a robust non-convex invariant set, given by the union of multiple ellipsoidal invariant sets, and a nonlinear backup control law, given by the combination of multiple stabilizing linear feedbacks, are computed offline. In presence of unsafe inputs, the safety framework applies the backup control law, preventing the system to violate the constraints. As the robust invariant set and the backup stabilizing controller are computed offline, the online operations reduce to simple function evaluations, which enables the use of the proposed framework on systems with limited computational resources. The capabilities of the safety framework are illustrated by three numerical examples.

中文翻译：

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使用基于不变性的安全框架的分布式安全学习

在不确定动态系统的大规模网络中，通信受限且子系统之间存在强相互作用，学习局部模型和控制策略为设计高性能控制器提供了巨大的潜力。同时，缺乏安全保证，这里以约束满足的形式考虑，阻止了数据驱动技术在安全关键分布式系统中的使用。本文提出了一个安全框架，可以在学习的同时保证不确定分布式系统的约束满足。该框架考虑了在动力学中具有耦合并受有界参数不确定性影响的线性系统，并利用鲁棒不变性来保证安全。特别是，一个鲁棒的非凸不变集，由多个椭球不变集的并集给出，离线计算由多个稳定线性反馈组合给出的非线性备用控制律。在存在不安全输入的情况下，安全框架应用后备控制律，防止系统违反约束。由于鲁棒不变集和备份稳定控制器是离线计算的，在线操作简化为简单的函数评估，这使得所提出的框架能够在计算资源有限的系统上使用。安全框架的能力通过三个数值例子来说明。由于鲁棒不变集和备份稳定控制器是离线计算的，在线操作简化为简单的函数评估，这使得所提出的框架能够在计算资源有限的系统上使用。安全框架的能力通过三个数值例子来说明。由于鲁棒不变集和备份稳定控制器是离线计算的，在线操作简化为简单的函数评估，这使得所提出的框架能够在计算资源有限的系统上使用。安全框架的能力通过三个数值例子来说明。