Reducing Computation Time with Priority Assignment in Distributed MPC

Distributing computations among agents in a networked control system (NCS) reduces computational effort. One distribution strategy is prioritized distributed model predictive control (P-DMPC). In P-DMPC, we couple and prioritize interacting agents to achieve a desired behavior of the NCS. We characterize the interaction with a directed acyclic graph (DAG). The computation time of the NCS is mainly determined through the longest path in the DAG. The longest path depends on the undirected coupling graph, which is fixed, and the prioritization, which is variable. The approaches to prioritize agents are numerous and pursue various goals. This article presents an approach to assign priorities in P-DMPC to reduce the longest path length in the coupling DAG and thus the computation time for the NCS. We prove that this problem can be mapped to a graph-coloring problem, in which the number of colors required corresponds to the longest path length in the coupling DAG. We further propose to reorder the colors, which decreases the number of constraints for agents along the longest path in the coupling DAG. We propose a decentralized graph-coloring algorithm to determine priorities for the agents. We evaluate the approach by applying it to trajectory planning for networked and autonomous vehicles on roads.