On the Link Between Multi-Coloring Problems for Graphs and Distributed Supervision of Interconnected Systems

this paper the link between Graph colorability theory and the design of a distributed Command Governor (CG) strategy is investigated. The first link between distributed supervision of systems with constraints and colorability properties was highlighted in a previous work where the idea of Turnbased CG was introduced for dynamically decoupled systems subject to coupling constraints. In this paper we will extend such a scheme to the case of dynamically coupled systems and we will show that the problem of determining the the minimal number of turns along with maximization of the agents appearance in turns is equivalent to a particular graph coloring problem. Such a problem is presented in a formal way and its complexity properties deeply discussed. A final example is presented to illustrate the effectiveness of the proposed strategy.