Graph Neural Networks for Distributed Linear-Quadratic Control
Graph Neural Networks for Distributed Linear-Quadratic Control
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发表时间：
2020-11
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通讯作者：
Fernando Gama;S. Sojoudi
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作者：
Fernando Gama;S. Sojoudi
线性二次控制器是控制理论中的基本问题之一。最佳解决方案是线性控制器，它需要在任何给定时间访问整个系统的状态。当考虑网络系统时，这使得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分布式控制器，其中系统的不同组件仅基于本地信息进行控制。与经典的集中式情况不同，获得最优分布式控制器通常是一个棘手的问题。因此，我们采用图神经网络（GNN）作为分布式控制器的参数化。 GNN 本质上是局部的并且具有分布式架构，这使得它们非常适合学习非线性分布式控制器。通过将线性二次问题转化为自监督学习问题，我们能够找到最好的基于 GNN 的分布式控制器。我们还推导了所得闭环系统稳定的充分条件。我们进行了广泛的模拟来研究基于 GNN 的分布式控制器的性能，并展示它们是一种具有可扩展性和可转移能力的计算高效的参数化。
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.