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Given an ensemble of autonomous agents and a task to achieve cooperatively,how much do the agents need to know about the state of the ensemble and aboutthe task in order to achieve it? We introduce new methods to understand theseaspects of decentralized control. Precisely, we introduce a framework tocapture what agents with partial information can achieve by cooperating andillustrate its use by deriving results about global stabilization of directedformations. This framework underscores the need to differentiate the knowledgean agent has about the task to accomplish from the knowledge an agent has aboutthe current state of the system. The control of directed formations has provento be more difficult than initially thought, as is exemplified by the lack ofglobal result for formations with n \geq 4 agents. We established in part Ithat the space of planar formations has a non-trivial global topology. Wepropose here an extension of the notion of global stability which, because itacknowledges this non-trivial topology, can be applied to the study offormation control. We then develop a framework that reduces the question ofwhether feedback with partial information can stabilize the system to whethertwo sets of functions intersect. We apply this framework to the study of adirected formation with n = 4 agents and show that the agents do not haveenough information to implement locally stabilizing feedback laws.Additionally, we show that feedback laws that respect the information flowcannot stabilize a target configuration without stabilizing other, unwantedconfigurations.

Decentralized Formation Control Part II: Algebraic aspects of information flow and singularities