Large-scale cyber-physical systems require that control policies are distributed, that is, that they only rely on local real-time measurements and communication with neighboring agents. Optimal Distributed Control (ODC) problems are, however, highly intractable even in seemingly simple cases. Recent work has thus proposed training Neural Network (NN) distributed controllers. A main challenge of NN controllers is that they are not dependable during and after training, that is, the closed-loop system may be unstable, and the training may fail due to vanishing and exploding gradients. In this paper, we address these issues for networks of nonlinear port-Hamiltonian (pH) systems, whose modeling power ranges from energy systems to non-holonomic vehicles and chemical reactions. Specifically, we embrace the compositional properties of pH systems to characterize deep Hamiltonian control policies with built-in closed-loop stability guarantees, irrespective of the interconnection topology and the chosen NN parameters. Furthermore, our setup enables leveraging recent results on well-behaved neural ODEs to prevent the phenomenon of vanishing gradients by design. Numerical experiments corroborate the dependability of the proposed architecture, while matching the performance of general neural network policies.
翻译:大型大型网络物理系统要求分散控制政策,也就是说,它们只能依靠当地实时测量和与邻近物剂的通信。不过,最佳分布式控制(ODC)问题即便在看似简单的情况下也是非常棘手的。最近的工作因此建议培训神经网络分布控制器。NNN控制器的主要挑战是,在培训期间和之后,它们不能可靠,也就是说,封闭环状系统可能不稳定,培训可能由于渐变消失和爆炸而失败。在本文件中,我们处理非线性港-哈米尔顿(PH)系统网络的这些问题,这些网络的模型化动力范围从能源系统到非热层车辆和化学反应不等。具体地说,我们接受PH系统的组成特性,用封闭式封闭式通道稳定性保证来描述密尔密尔顿控制政策的特征,而不论互连地表和选择的NNW参数如何。此外,我们的设置使得最近的结果能够借助于妥善管理的神经系统,防止通过设计来消逝动神经梯度现象的现象。Nummerical 实验同时取决于拟议的总体结构的性能。