论文标题
用于分布式线性季节控制的图形神经网络
Graph Neural Networks for Distributed Linear-Quadratic Control
论文作者
论文摘要
线性季度控制器是控制理论中的基本问题之一。最佳解决方案是一个线性控制器，需要在任何给定时间访问整个系统的状态。在考虑网络系统时，这将使最佳控制器成为集中式控制器。网络系统的互连性质通常需要一个分布式控制器，其中仅根据本地信息来控制系统的不同组件。与经典的集中式案例不同，获得最佳分布控制器通常是一个棘手的问题。因此，我们采用图形神经网络（GNN）作为分布式控制器的参数化。 GNN自然是本地的，并且具有分布式架构，使其非常适合学习非线性分布式控制器。通过将线性二次问题抛弃为一个自我监督的学习问题，我们可以找到最佳的基于GNN的分布式控制器。我们还得出了足够的条件，使所得的闭环系统保持稳定。我们进行了广泛的模拟，以研究基于GNN的分布式控制器的性能，并展示它们是具有可伸缩性和可传递性功能的计算有效的参数化。
The linear-quadratic controller is one of the fundamental problems in control theory. The optimal solution is a linear controller that requires access to the state of the entire system at any given time. When considering a network system, this renders the optimal controller a centralized one. The interconnected nature of a network system often demands a distributed controller, where different components of the system are controlled based only on local information. Unlike the classical centralized case, obtaining the optimal distributed controller is usually an intractable problem. Thus, we adopt a graph neural network (GNN) as a parametrization of distributed controllers. GNNs are naturally local and have distributed architectures, making them well suited for learning nonlinear distributed controllers. By casting the linear-quadratic problem as a self-supervised learning problem, we are able to find the best GNN-based distributed controller. We also derive sufficient conditions for the resulting closed-loop system to be stable. We run extensive simulations to study the performance of GNN-based distributed controllers and showcase that they are a computationally efficient parametrization with scalability and transferability capabilities.
