A distributed command governor based on graph colorability theory

In this paper, a distributed command governor (CG) strategy is introduced that, by the use of graph colorability theory, improves the scalability property and the performance of recently introduced distributed noncooperative sequential CG strategies. The latter are characterized by the fact that only 1 agent at a decision time is allowed to update its command, whereas all the others keep applying their previously computed commands. The scalability of these early CG distributed schemes and their performance are limited because the structure of the constraints is not taken into account in their implementation. Here, by exploiting the idea that agents that are not directly coupled by the constraints can simultaneously update their control actions, the agents in the network are grouped into particular subsets (turns). At each time instant, on the basis of a round-robin policy, all agents belonging to a turn are allowed to update simultaneously their commands, whereas agents in other turns keep applying their previous commands. Then, a turn-based distributed CG strategy is proposed and its main properties are analyzed. Graph colorability theory is used to determine the minimal number of turns and to distribute each agent in at least a turn. A novel graph colorability problem that allows one to maximize the frequency at which agents can update their commands is proposed and discussed. A final example is presented to illustrate the effectiveness of the proposed strategy.