Graph Neural Network-Based Distributed Optimal Control for Linear Networked Systems: An Online Distributed Training Approach
This addresses the need for resilient, distributed control in networked systems, offering an incremental improvement over existing centralized and offline methods.
The paper tackles the problem of learning distributed optimal controllers for linear networked systems using graph recurrent neural networks (GRNNs), achieving online distributed training with local closed-loop stability guarantees.
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.