  The implementation feasibility of control algorithms over very large-scale
networks calls for hard constraints regarding communication, computational, and
memory requirements. In this paper, the decentralized receding horizon control
problem for very large-scale networks of dynamically decoupled systems with a
common, possibly time-varying, control objective is addressed. Each system is
assumed to be modeled by linear time-varying dynamics, which can be leveraged
to approximate nonlinear systems about successive points of operation. A
distributed and decentralized receding horizon control solution is put forward,
which: i) takes communication delays into account; ii) allows local
communication exclusively; and iii) whose computational and memory requirements
in each computational unit do not scale with the dimension of the network. The
scalability of the proposed solution enables emerging very large-scale
applications of swarm robotics and networked control. This approach is applied
to the orbit control problem of low Earth orbit mega-constellations, featuring
high-fidelity numerical simulations for the Starlink mega-constellation.
