用图神经网络实现在线分布式控制，提升网络系统韧性。
Graph Neural Network-Based Distributed Optimal Control for Linear Networked Systems: An Online Distributed Training Approach
- 用图循环神经网络建模分布式控制器，转化为自监督学习问题。
- 通过分布式梯度计算实现在线训练，无需中心化协调。
- 理论保证局部闭环稳定性，适合大规模网络系统实时控制。
本文研究离散时间线性网络化系统的分布式最优控制问题。重点是利用图循环神经网络（GRNN）学习分布式最优控制器。现有方法多生成集中式控制器且需离线训练。随着对网络韧性的需求增加，控制器需具备分布式特性，并期望采用在线分布式方式训练，这正是本文的主要贡献。为此，我们提出基于GRNN的分布式最优控制方法，将问题转化为自监督学习问题；通过分布式梯度计算实现在线训练，受共识型分布式优化启发，设计了分布式在线训练优化器；在假设GRNN控制器的非线性激活函数同时满足局部扇区有界和斜率受限的前提下，给出了系统局部闭环稳定性的理论保证。通过专门开发的仿真器进行数值实验，验证了所提方法的有效性。
原文摘要 · Abstract (English)
In this paper, we consider the distributed optimal control problem for discrete-time linear networked systems. In particular, we are interested in learning distributed optimal controllers using graph recurrent neural networks (GRNNs). Most of the existing approaches result in centralized optimal controllers with offline training processes. However, as the increasing demand of network resilience, the optimal controllers are further expected to be distributed, and are desirable to be trained in an online distributed fashion, which are also the main contributions of our work. To solve this problem, we first propose a GRNN-based distributed optimal control method, and we cast the problem as a self-supervised learning problem. Then, the distributed online training is achieved via distributed gradient computation, and inspired by the (consensus-based) distributed optimization idea, a distributed online training optimizer is designed. Furthermore, the local closed-loop stability of the linear networked system under our proposed GRNN-based controller is provided by assuming that the nonlinear activation function of the GRNN-based controller is both local sector-bounded and slope-restricted. The effectiveness of our proposed method is illustrated by numerical simulations using a specifically developed simulator.
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