Distributed decentralized receding horizon control for very large-scale networks with application to satellite mega-constellations

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.