  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.
