New Results on Supervisor Localization, with Application to Multi-Agent Formations

Recently we developed supervisor localization, a top-down approach to distributed control of discrete-event systems in the Ramadge-Wonham supervisory control framework. Its essence is the allocation of monolithic (global) control action among the local control strategies of individual agents. In this paper, we start by presenting several refinements of our localization theory. First, we drop the original assumption that the event sets of component agents are pairwise disjoint. Second, we show that consistent marking information can be enforced by just one agent, which can be selected arbitrarily. Third, the event sets of localized controllers are explicitly defined, in general as proper subsets of the entire event set. For these generalizations, we again prove that the collective local controlled behavior is identical to the global optimal and nonblocking controlled behavior. We go on to apply supervisor localization to solve a multi-agent formation problem. A suitable formulation of convergence to formations is first introduced; then local strategies are synthesized for a group of agents to arrive at an arbitrarily pre-specified formation, and issues of information exchange and control logic are examined.